Keywords:Optimal control, Predictive control for nonlinear systems, Optimization Abstract: The concept of dynamic-mean Pareto optimality is introduced for multi-objective Model Predictive Control. Dynamic-mean Pareto optimal solutions are obtained by solving a free initial state and final time optimal control problem. Subsequently, we propose a receding horizon tracking formulation with dynamic-mean Utopia set-points. A Dynamic-mean Utopia point is defined as the intersection of average minima, of underlying performance indices, over a dynamic horizon. The latter is compared with recently proposed steady-state Utopia tracking and Pareto optimally weighted Economic MPC. Incorporating dynamic-mean Utopia set-points in a tracking formulation, one attains economic performance at least equal to that of steady-state Utopia tracking, and, performance close to that of Pareto optimal, weighted Economic MPC. The latter is illustrated for a CSTR numerical case example.

Keywords:Optimization, Computer aided control design, Predictive control for linear systems Abstract: This paper describes a framework for generating easily verifiable code to solve convex optimization problems in embedded applications by transforming them into equivalent second-order cone programs. In embedded applications, it is critical to be able to verify code correctness, but it is also desirable to be able to rapidly prototype and deploy high-performance solvers for different problems. To balance these two requirements, we propose a code generation system that takes high-level descriptions of convex optimization problems and generates code that maps the parameters in the original problem to data in an equivalent second-order cone program, which is then solved by a single, external solver that can be verified once and for all. A novel aspect is that we restrict the parameters in the original problem to only appear in affine functions, which lets us map the parameters to problem data without performing any floating point operations. As a result, the generated code is lightweight, fast, and trivial to verify. The approach thus marries the benefits of high-level parser/solvers with custom, high-performance, high-reliability solvers for embedded applications.

Keywords:Predictive control for linear systems, Sampled data control, Optimization algorithms Abstract: This paper presents an efficient computational method for solving the input-constrained, continuous time, infinite horizon, linear quadratic regulator problem to within a user specified tolerance. The infinite dimensional input trajectory is approximated with a piecewise linear function on a finite time discretization to ensure input constraint satisfaction. This approximate problem is then a standard finite dimensional quadratic program and is solved by conventional methods, generating an upper bound for the optimal value function. The finite time discretization is then refined by subdividing the intervals estimated to cause the largest decrease in the cost function. Convergence of the solution of this discretized problem towards the optimal continuous-time solution, as the discretization is refined, is proved. Exploiting the strict convex- ity of the original infinite dimensional problem, the gradient of the cost function with respect to the continuous-time input can be computed to generate a lower bound for the optimal cost. For computational efficiency, a lower bound for the solution of the discretized control at a very fine discretization can be used instead. The algorithm terminates when the difference between the upper and lower bounds meets a user supplied tolerance.

Keywords:Predictive control for linear systems, Constrained control, Optimization Abstract: This paper proposes a model predictive control scheme to provide temperature set-points to thermostatic controlled cooling units in refrigeration systems. The control problem is formulated as a convex programming problem to minimize the overall operating cost of the system. The foodstuff temperatures are estimated by reduced order observers and evaporation temperature is regulated by an algorithmic suction pressure control scheme. The method is applied to a validated simulation benchmark. The results show that even with the thermostatic control valves, there exists significant potential to reduce the operating cost.

Keywords:Supervisory control, Predictive control for linear systems, Optimization Abstract: A model predictive control at supervisory level is proposed for refrigeration systems including distributed local controllers. Prediction of the electricity price and outdoor temperature are assumed available. The control objective is to minimize the overall energy cost within the prediction horizon. The method is mainly developed for demand-side management in the future smart grid, but a simpler version can be applied in the current electricity market. Due to the system nonlinearity, the minimization is in general a complicated nonconvex optimization problem. A new supervisory control structure as well as an algorithmic pressure control scheme is presented to rearrange the problem to facilitate convex programming. A nonlinear continuous time model validated by real data is employed to simulate the system operation. The results show a considerable economic saving as well as a trade-off between the saving level and the design complexity.

Keywords:Process control, Predictive control for linear systems Abstract: Model Predictive Control is an algorithm commonly used in the petrochemical and chemical sectors to control large processes. Its success can be traced to the fact that it is MIMO control algorithm with intrinsic dead-time compensation, capacity to handle the process’ constraints and with tuning parameters that are easily understandable in the time domain. Nevertheless, its usage is limited to large processes where the investment in the currently expensive advanced control systems are economically viable. Thus, this work proposes a low cost embedded MPC controller targeted at companies with medium and small processes that could have production improvements with the use of MPC. This paper details the current embedded system prototype and the results obtained with a hardware-in-the-loop experiment of an ethanol distillation process simulator.

Keywords:Distributed parameter systems Abstract: The main thrust of this work is on the penalization of the pairwise state estimates used to enforce consensus in spatially distributed filters. It is assumed that a spatially distributed process has a network of in-domain sensors with spatially distributed filters corresponding to each sensor in the network. To better improve the agreement of the distributed filters, the spatial gradient of the pairwise difference of state estimates is used as a means to penalize their disagreement. Additionally, a proportional penalization and an integral penalization for the pairwise differences are also examined in order to lay down the foundation for a spatial proportional- integral-derivative penalization of the spatially distributed filters. Addressing the partial connectivity issue, a condition that resembles the Lagrangian potential for infinite dimensional systems is given in terms of the inner product of the state errors and their pairwise differences. In a forward looking approach, the extension to a more general class of partial differential equations, written as evolution equations in an appropriate Hilbert space, are examined and the conditions regarding the network connectivity are expressed as conditions on the inner product of the consensus operator and the pairwise difference of the state estimation errors.

Keywords:Distributed parameter systems, Automotive, Delay systems Abstract: This paper proposes a model for the internal temperature of a SI engine catalyst, aiming at designing a prediction-based light-off strategy. Due to its elongated geometry where a gas stream is in contact with a spatially distributed monolith, the system under consideration is inherently a distributed parameter system. This paper advocates an approach which is based on a one-dimensional distributed parameter model, coupled with an advection-diffusion equation accounting for the distributed heat generation resulting from pollutant conversion. Following recent works, this heat supply is shown here to be equivalent to an inlet temperature entering the system at a virtual entry point inside the catalyst. This new input has a static gain depending on the state of the system, which introduced a coupling. Taking advantage of the low-pass filter characteristic of the system, an estimate of this model is designed and results into a time-varying input-delay system whose dynamics parameters (time constant, delay, gains) are obtained through a simple analytic reduction procedure. A corresponding prediction-based light-off strategy is proposed and illustrated in simulations exploiting experimental data.

Keywords:Distributed parameter systems, Identification Abstract: Parameter identification in infinite-dimensional systems with lumped measurements is considered. The proposed method is based on a convolutional input-output relation of the underlying system of partial differential equations. The derivation of this input-output relation is presented in a framework involving (ultra-)distributions. The unknown parameters are determined by minimizing an associated error functional.

Keywords:Distributed parameter systems, Observers for linear systems Abstract: We investigate the boundary observer design problem for a class of linear first-order hyperbolic systems on a finite space domain with spatially varying parameters. The system features one negative transport speed and an arbitrary fixed number n of positive transport speeds. Using a backstepping approach, the distributed states are estimated from a single boundary measurement, as illustrated in presented numerical simulations.

Keywords:Distributed parameter systems, Observers for nonlinear systems Abstract: An extended Luenberger observer is proposed for the solution of the state estimation problem for semi-linear parabolic PDEs with reactive-convective non-linearities. Here, the backstepping method is applied to the linearised observer error dynamics to determine the observer gains. This, however, requires a successive evaluation of the so-called Hopf-Cole transformation allowing to transform the PDE of the linearised observer error into a normal form, for which backstepping can be directly used. Moreover, the computational efficiency of determination of the gains is improved by combining the direct numerical solution approach with the sample-and-hold implementation. Finally, the observer error convergence is analysed both theoretically and by means of numerical simulations.

Keywords:Distributed parameter systems, Identification, Optimization algorithms Abstract: The design of a network of observation nodes in a spatial domain is addressed. The observations are to be used to estimate unknown parameters of a distributed parameter system. Given a finite number of possible sites at which to locate a sensor, the problem is formulated as the selection of the gauged sites so as to minimize a convex criterion defined on the Fisher information matrix associated with the estimated parameters. The search for an optimal solution to this binary optimization problem is performed through solving a relaxed problem in which a constrained discrete probability distribution on the set of all allowable sites is sought. The main contribution here consists in properly parallelizing this solution using the parallel variable distribution approach. As a result, each processor minimizes a convex function subject to linear constraints through the use of a simplicial decomposition algorithm. The resulting individual solutions are then synchronized by finding their optimal convex combination.

Keywords:Distributed estimation over sensor nets, Large-scale systems, Stochastic filtering Abstract: State fusion is a method for merging multiple estimates of the same state into a single fused estimate. Dealing with multiple estimates is one of the main concerns in distributed state estimation, where an estimated value of the desired state vector is computed in each node of a networked system. Most solutions for distributed state estimation currently available assume that every node computes an estimate of the (same) global state vector. This assumption is impractical for systems observing large-area processes, due to the sheer size of the process state. A feasible solution is one where each node estimates a part of the global state vector, allowing different nodes in the network to have overlapping state elements. Although such an approach should be accompanied by a corresponding state fusion method, existing solutions cannot be employed as they merely consider fusion of two different estimates with emph{equal} state representations. Therefore, an empirical solution is presented for fusing two state estimates that have partially overlapping state elements. A justification of the proposed fusion method is presented, along with an illustrative case study for observing the temperature profile of a large rod, though a formal derivation is future research.

Keywords:Observers for linear systems, Adaptive systems, Stochastic filtering Abstract: This paper addresses the problem of adaptive state and parameter estimation of open loop unstable plants using a multiple model structure. A state estimate is obtained as a probabilistically weighted sum of the estimates produced by a bank of individual observers. Model identification and convergence of the dynamic weights in the Multiple Model Adaptive Estimation (MMAE) for open-loop unstable plants are analyzed and the effect of the control action (by a controller in the loop) is studied. In the present paper we show that the techniques introduced in MMAE for open-loop stable plants and in the absence of control action are applicable to open-loop unstable plants with a stabilizing controller in the loop. A distance-like pseudo norm between the true plant and the identified model is developed and furthermore we show that the model identified is the one that is the closest to the true plant model in the defined norm among all models in the bank. The performance and convergence of the MMAE procedure are illustrated with Monte-Carlo simulation runs using the model of an inverted pendulum installed on a system of masses, springs, and dampers.

Keywords:Stochastic filtering, Stochastic systems, Uncertain systems Abstract: In this paper the relation between nonanticipative rate distortion function (RDF) and Bayesian filtering theory is investigated using the topology of weak convergence of probability measures on Polish spaces. The relation is established via an optimization on the space of conditional distributions of the so-called directed information subject to fidelity constraints. Existence of the optimal reproduction distribution of the nonanticipative RDF is shown, while the optimal nonanticipative reproduction conditional distribution for stationary processes is derived in closed form. The realization procedure of nonanticipative RDF which is equivalent to joint-source channel matching for symbol-by-symbol transmission is described, while an example is introduced to illustrate the concepts.

Keywords:Stochastic filtering Abstract: We revisit the equivalent linearization technique to clarify a relationship between the extended Kalman filter (EKF) and equivalent linearization Kalman filter (EqKF). By deriving the equivalent gain for a static nonlinearity, we show that the equivalent linearization for the EqKF is a global method, though the first-order linearization for the EKF is a local one. Then, we consider discrete-time cubic sensor problems and analyze the Kalman gains and filtered covariances of respective filters, showing that the EqKF is quite close to the Gaussian filter (GF). Moreover, numerical results are included to compare the performances of the EqKF, EKF and GF.

Keywords:Stochastic filtering, Discrete event systems, Petri nets Abstract: The main objective of this article is to synthesize a particle filter algorithm for max-plus systems. It is presented a brief introduction to the max-plus approach for Discrete Event Systems. Next, the fundamentals of the particle filter and the way in which they can be applied to max-plus systems are presented. It leads to the algorithm for particles filtering. Lastly, some examples are given. The results shows the accuracy of the method and the improvements in comparison with the deterministic observer.

Keywords:Stochastic filtering, Process control, Observers for nonlinear systems Abstract: Drilling into offshore deep water, high-pressure high-temperature reservoirs is a very challenging process. The most important task in these drilling operations is to control bottomhole pressure. Many automatic control systems for drilling operations are based on models calculating wellbore pressure, flow and downhole hydraulics. Closed loop control systems, for example Managed Pressure Drilling, are examples of systems that may involve such real-time calculations. Therefore a high degree of accuracy in pressure and flow predictions is crucial to the performance of automatic drilling applications. In this paper the key uncertain model parameters and the bottom-hole pressure are estimated using joint unscented Kalman filter based on only available top-side measurements. The results of simulations show accurate estimation of the bottom-hole pressure and uncertain parameters, even in transient periods for example the scenario of pipe connection operations, where there is no available bottom-hole pressure measurement, and flow through the bit.

Keywords:Hybrid systems, Large-scale systems, Stability of hybrid systems Abstract: The paper addresses the question of a composition and decomposition of hybrid systems. Motivated by a simple example, we propose an extended definition of a hybrid system that allows for a natural and simple way to consider an interconnection of several hybrid systems as one hybrid system and to decompose one large hybrid system in a composition of several ones. A stability result and existence of solutions for the new framework are shown.

Keywords:Hybrid systems, LMI's/BMI's/SOS's, Stability of hybrid systems Abstract: Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finite-time asymptotic stability, and corresponding Lyapunov theorems have been developed. In this paper, we propose a method to construct Lyapunov functions to prove Zeno stability of compact sets in cyclic hybrid systems with parametric uncertainties in the vector fields, domains and guard sets, and reset maps utilizing sum-of-squares programming. This technique can easily be applied to cyclic hybrid systems without parametric uncertainties as well. Examples illustrating the use of the proposed technique are also provided.

Keywords:Hybrid systems, Switched systems, Constrained control Abstract: In this paper we will provide algebraic necessary and sufficient conditions for the controllability/reachability/null controllability of a class of bimodal discrete-time piecewise linear systems including several instances of interest that are not covered by existing works which focus primarily on the planar case. In particular, the class is characterized by a continuous right-hand side, a scalar input and a transfer function from the control input to the switching variable with at most two zeroes whereas the state can be of any dimension. To arrive at the main result, we will make use of geometric control theory for linear systems and a novel result on controllability for input-constrained linear systems with non-convex constraint sets.

Keywords:Hybrid systems, Uncertain systems, Constrained control Abstract: We investigate the recently introduced bang-bang funnel controller with respect to its robustness to time delays. We present slightly modified feasibility conditions and prove that the bang-bang funnel controller applied to a relative-degree-two nonlinear system can tolerate sufficiently small time delays. A second contribution of this paper is an extensive case study, based on a model of a real experimental setup, where implementation issues such as the necessary sampling time and the conservativeness of the feasibility assumptions are explicitly considered.

Keywords:Observers for linear systems, Hybrid systems, Biological systems Abstract: This paper deals with state estimation in linear time-invariant systems subject to unknown impulsive input signals. A solution based on a linear impulsive observer and a finite-memory convolution operator is suggested. The problem arises e.g. in the context of systems with intrinsic pulse-modulated feedback that have recently been applied to mathematical modeling of endocrine systems with pulsatile hormone secretion. Simulation results illustrating the performance of the proposed method are provided.

Keywords:Stability of hybrid systems, Constrained control, Lyapunov methods Abstract: In this paper, some tools for the analysis of a class of hybrid control systems for a continuous-time plant with input magnitude saturation are presented. We show that certain continuous-time LMI-based techniques can be extended to this setting when a dwell-time property is satisﬁed by the hybrid loop. Moreover, for the case in which the hybrid controller has the same order as the plant, the synthesis of a static direct linear anti-windup (DLAW) compensator is proposed. The need of including the ﬂow and jump sets in the analysis and synthesis conditions leads to LMIs for global results, that is, when the plant is exponentially stable and BMIs otherwise.

Keywords:Stability of hybrid systems Abstract: Reset control is introduced to overcome limitations of linear control. A reset controller includes a linear controller which resets some of states to zero when their input is zero or certain non-zero values. This paper studies the application of the fractional-order Clegg integrator (FCI) and compares its performance with both the commonly used first order reset element (FORE) and traditional Clegg integrator (CI). Moreover, stability of reset control systems is generalized for the fractional-order case. Two examples are given to illustrate the application of the stability theorem.

Keywords:Nonlinear system theory, Optimization algorithms, LMI's/BMI's/SOS's Abstract: An extension of the Krylov-Bogoliubov method and of the harmonic linearization method for approximating second order nonlinear systems with fast variation of damping factor and frequency of oscillation is revisited and a solution method involving a power series approach is proposed, which makes it easy for the extended asymptotic method to be applied to other damped nonlinear systems. Furthermore, the application of the method to the analysis of the decay rate of the nonlinear solution is presented. A performance measure for the analysis of the decay rate for nonlinear systems is proposed and exemplified on two nonlinear control algorithms, linear constrained control and constrained soft variable structure control with implicit Lyapunov functions.

Keywords:Nonlinear system theory, Stability of nonlinear systems, Behavioural systems Abstract: We consider the development of a general nonlinear small-gain theorem for systems with abstract initial conditions. Systems are defined in a set theoretic manner from input-output pairs on a doubly infinite time axis, and a general construction of the initial conditions (i.e. a state at time zero) is given in terms of an equivalence class of trajectories on the negative time axis. By using this formulation, an ISS-type nonlinear small-gain theorem is established with complete disconnection between the stability property and the existence, uniqueness properties. We provide an illustrative example.

Keywords:Stability of nonlinear systems, Lyapunov methods, Robust control Abstract: Several conditions are proposed to check input-to-state stability (ISS) and integral input-to-state stability (iISS) properties for generic nonlinear systems applying the weighted homogeneity concept (global or local). The advantages of this result is that, under some mild conditions, the system robustness can be established as a function of the degree of homogeneity.

Keywords:Stability of nonlinear systems, Nonlinear system theory Abstract: Recent results in equivalence between classes of multipliers for slope-restricted nonlinearities are extended to multipliers for bounded and monotone nonlinearities. This extension requires a slightly modified version of the Zames--Falb theorem and a more general definition of phase--substitution. The results in this paper resolve apparent contradictions in the literature on classes of multipliers for bounded and monotone nonlinearities.

Keywords:Algebraic/geometric methods, Constrained control, Optimal control Abstract: This paper derives explicit solutions for Riemannian and sub-Riemannian curves on non-Euclidean spaces of arbitrary cross-sectional curvature. The problem is formulated in the context of an optimal control problem on a 3-D Lie group and an application of Pontryagin's maximum principle of optimal control leads to the appropriate quadratic Hamiltonian. It is shown that the regular extremals defining the necessary conditions for Riemannian and sub-Riemannian curves can each be expressed as the classical simple pendulum. The regular extremal curves are solved analytically in terms of Jacobi elliptic functions and their projection onto the underlying base space of arbitrary curvature are explicitly derived in terms of Jacobi elliptic functions and an elliptic integral.

Keywords:Algebraic/geometric methods, Nonlinear system theory Abstract: We consider local observability of discrete-time polynomial systems. When testing local observability of nonlinear systems, the observability rank condition is commonly used. However, the rank condition is only a sufficient condition in general. For this problem, recently, in terms of commutative algebra and algebraic geometry, a necessary condition for local observability of the polynomial systems has been derived. In this paper, we show the necessary condition is a sufficient condition for local observability for almost all initial states. Based on this result, we derive a necessary and sufficient condition for local observability.

Keywords:Algebraic/geometric methods, Output feedback, Feedback linearization Abstract: The problem of input-output linearization by dynamic output feedback of discrete-time multi-input multi-output nonlinear control systems is considered in this paper. The system is described by the set of higher order input-output difference equations. First, an algorithm is given to find a set of functions, which are then used to provide sufficient solvability conditions and the equations of the dynamic output feedback. The results are specified for the special subclass of systems, called ANARX systems and comparisons with the single-input single-output case is made.

Keywords:Feedback linearization, Algebraic/geometric methods, Observers for nonlinear systems Abstract: Given a class of nonlinear systems with implicitly defined outputs, we provide a new algorithm to find appropriate local coordinates, in which the resulting system takes a desired target form that is state-affine, up to output and input injection. Once in the target form, it is possible to construct a state-space observer with linear, possibly time-varying, error dynamics.

Keywords:Optimal control, Differential algebraic systems, Behavioural systems Abstract: We study Hamiltonian systems, namely, systems comprising of trajectories which are `stationary' with respect to a quadratic performance index: they play a central role in many optimal control problems. A typical assumption in the literature is that of `regularity': the resulting first-order dynamical system is a regular state space system and not a singular descriptor system. In this paper we show that the first order representation of a Hamiltonian is a singular descriptor system if and only if the interconnection of a related MIMO system G(s) with its dual (i.e. its adjoint) is ill-posed. We address the possibility of existence of inadmissible initial conditions, i.e. initial conditions that give rise to impulsive solutions. We characterize conditions on G(s) under which the corresponding singular Hamiltonian system has inadmissible initial conditions. Under suitable simplifying assumptions, which amount to studying an extreme case of ill-posedness, our main result states that there exist no inadmissible initial conditions if and only if the skew-symmetric part of the first moment about s equal to infinity of the transfer matrix G(s) is nonsingular; a condition we show that is opposite to that for G(s) to be an all-pass filter. As a corollary, ill-posed interconnection of a square MIMO system with odd number of inputs (in particular, SISO systems) with its adjoint always contains in inadmissible initial conditions.

Keywords:Stability of nonlinear systems, Algebraic/geometric methods Abstract: Recent developments in the attitude control of a rigid body include the development of almost globally stabilizing coordinate-free control laws. However, all of these results focus on external actuation. In this paper, we first observe that the frequently used way of stabilization by error functions can also be given a Hamiltonian interpretation. We then show that there exists a class of control laws which are applicable for both external and internal actuation.

Keywords:Concensus control and estimation, Cooperative autonomous systems, Cooperative control Abstract: We propose two distributed algorithms, one for solving the weight-balance problem and another for solving the bistochastic matrix formation problem, in a distributed system whose components (nodes) can exchange information via interconnection links (edges) that form an arbitrary, possibly directed, strongly connected communication topology (digraph). Both distributed algorithms achieve their goal asymptotically and operate iteratively by having each node adapt the (nonnegative) weights on its outgoing edges based on the weights of its incoming links. The weight-balancing algorithm is shown to admit geometric convergence rate, whereas the second algorithm, which is a modification of the weight-balancing algorithm, leads asymptotically to a bistochastic digraph with geometric convergence rate for a certain set of initial values. The two algorithms perform better than existing approaches, as illustrated by the examples we provide.

Keywords:Agents networks, Concensus control and estimation, Cooperative autonomous systems Abstract: This paper proposes two continuous-time dynamic average consensus algorithms for networks with strongly connected and weight-balanced interaction topologies. The proposed algorithms, termed 1st-Order-Input Dynamic Consensus (FOI-DC) and 2nd-Order-Input Dynamic Consensus (SOI-DC), respectively, allow agents to track the average of their dynamic inputs within an O(epsilon)-neighborhood with a pre-specified rate. The only requirement on the set of reference inputs is having continuous bounded derivatives, up to second order for FOI-DC and up to third order for SOI-DC. The correctness analysis of the algorithms relies on singular perturbation theory for non-autonomous dynamical systems. When dynamic inputs are offset from one another by static values, we show that SOI-DC converges to the exact dynamic average with no steady-state error. Simulations illustrate our results.

Keywords:Distributed cooperative control over networks, Concensus control and estimation, Cooperative control Abstract: This paper presents consensus problems over IEEE 802.15.4 wireless networks. The IEEE 802.15.4 protocol defines the Medium Access Control (MAC) and the physical layer (PHY) for Low-Rate Wireless Personal Area Networks (LR-WPANs). The IEEE 802.15.4 MAC protocol supports the beacon-enabled mode that enables real-time communication by allocating Guaranteed Time Slots (GTSs) to a designated node in a network. Despite a number of work on cooperative control, consensus problems over wireless networks remains less well understood. In this paper, we propose a modified version of the standard IEEE 802.15.4 protocol where each agent communicates through a PAN coordinator with a superframe structure. We consider a branch-and-bound GTS scheduling algorithm for non-preemptive communication tasks under the modified IEEE 802.15.4 protocol. The simulation result shows that each agent can successfully communicate with each other and achieve a consensus by the proposed GTS scheduling algorithm.

Keywords:Distributed cooperative control over networks, Cooperative autonomous systems, Agents networks Abstract: This paper investigates the consensus for multiple interacting clusters of double-integrator agents under two different frameworks, viz, the framework that all agents share the same position and velocity interaction topology and the framework that the position and velocity topologies are modeled by totally independent graphs. Different cluster consensus algorithms are designed and analyzed accordingly. A consistent structural result is shown for both frameworks that cluster consensus can be reached if the interaction topologies satisfy some connectivity assumptions and further, compared to the interactions among different clusters, the interactions within each cluster are sufficiently strong. Some lower bounds for such strengths are specified as well.

Keywords:Distributed estimation over sensor nets, Cooperative control Abstract: This paper regards the relative localization problem in sensor networks. We propose for its solution a distributed randomized algorithm, which is based on input-driven consensus dynamics and features pairwise “gossip” communications and updates. Due to the randomness of the updates, the state of this algorithm oscillates in time around a certain limit value. We show that the time-average of the state asymptotically converges, in the mean-square sense, to the least-squares solution of the localization problem. Furthermore, we describe an update scheme ensuring that the time-averaging process is accomplished in a fully distributed way.

Keywords:Distributed estimation over sensor nets, Distributed cooperative control over networks, Concensus control and estimation Abstract: In many randomized consensus algorithms, the constraint of average preservation may not be enforced at every time step, resulting in an error between the average of the initial conditions and the current average. We have recently shown that under mild conditions on the distribution of the update matrices, the mean square error has an upper bound inversely proportional to the size of the network. In this work, we consider the case of consensus with packet losses and interferences. Using an extension of our results taking correlations into account, we show that the MSE induced by losses and interferences can be estimated by such a bound: hence we argue that larger networks are naturally more robust, in terms of accuracy, to packet losses and interferences. Our results hold for general networks, without restrictive assumptions on its topology.

Keywords:Optimal control, UAV's Abstract: Solving the time-optimal path planning problem, where a system is brought from an initial to terminal state in minimal time while obeying geometric and dynamic constraints, has been an active area of research for many years. Very often the problem is divided into a high-level path planning stage where a feasible geometric path is determined and a low-level path following stage where system dynamics are taken into account. This paper combines both approaches for differentially flat systems into a single optimization problem. The geometric path is represented as a convex combination of two or more feasible paths and the dynamics of the system can subsequently be projected onto the path which leads to a single input system. The resulting optimization problem is transformed into a fixed end-time optimal control problem that can be initialized easily. Throughout the paper, the quadrotor, a challenging non-linear system, is used to illustrate the proposed approach.

Keywords:UAV's Abstract: In this paper the autonomous flight mode conversion control scheme for a Quad-TiltRotor Unmanned Aerial Vehicle is presented. This convertible UAV type has the capability for flying both as a helicopter as well as a fixed-wing aircraft type, by adjusting the orientation of its tilt-enabled rotors. Thus, a platform combining the operational advantages of two commonly distinct aircraft types is formed. However, its autonomous mid-flight conversion is an issue of increased complexity. The approach presented is based on an innovative control scheme, developed based on hybrid systems theory. Particularly, a piecewise affine modeling approximation of the complete nonlinear dynamics is derived and serves as the model for control over which a hybrid predictive controller that provides global stabilization, optimality and constraints satisfaction is computed. The effectiveness of the proposed control scheme in handling the mode conversion from helicopter to fixed-wing (and conversely) is demonstrated via a series of simulation studies. The proposed control scheme exceeds the functionality of the aforementioned flight-mode conversion and is also able to handle the transition to intermediate flight-modes with rotors slightly tilted forward in order to provide a forward force component while flying in close to helicopter-mode.

Keywords:Iterative learning control, Aerospace, Robotics Abstract: Quadrocopters allow the execution of high-performance maneuvers under feedback control. However, repeated execution typically leads to a large part of the tracking errors being repeated. This paper evaluates an iterative learning scheme for an experiment where a quadrocopter flies in a circle while balancing an inverted pendulum. The scheme permits the non-causal compensation of periodic errors when executing the circular motion repeatedly, and is based on a Fourier series decomposition of the repeated tracking error and compensation input. The convergence of the learning scheme is shown for the linearized system dynamics. Experiments validate the approach and demonstrate its ability to significantly improve tracking performance.

Keywords:UAV's, Robotics Abstract: This paper analyzes the application of admittance control to quadrocopters, focusing on physical human-vehicle interaction. Admittance control allows users to define the apparent inertia, damping, and stiffness of a robot, providing an intuitive way to physically interact with it. In this work, external forces acting on the quadrocopter are estimated from position and attitude information and then input to the admittance controller, which modifies the vehicle reference trajectory accordingly. The reference trajectory is appropriately tracked by an underlying position and attitude controller. The characteristics of the overall control scheme are investigated for the near-hover case. Experimental results complement the paper, demonstrating the suitability of the method for physical human-quadrocopter interaction.

Keywords:UAV's, Lyapunov methods, Adaptive control Abstract: This paper addresses the problem of designing and experimentally validating a controller for steering a quadrotor vehicle along a trajectory, while rejecting wind disturbances. The proposed solution consists of a nonlinear adaptive state feedback controller for thrust and torque actuation that asymptotically stabilizes the closed-loop system in the presence of constant force disturbances, used to model the wind action, and ensures that the actuation does not grow unbounded as a function of the position errors. A prototyping and testing architecture, developed to streamline the implementation and the tuning of the controller, is also described. Experimental results are presented to demonstrate the performance and robustness of the proposed controller.

Keywords:Cooperative control, UAV's, Lyapunov methods Abstract: This paper presents a strategy for formation control of autonomous vehicles using a leader-following approach. A trajectory planner prescribes the motion of a group of virtual vehicles, using a Lyapunov-based nonlinear controller that stabilizes the position of the leader in the reference frame of the virtual vehicles, at a predefined distance vector. This strategy differs from the standard approach of defining the desired distance vector in an inertial frame and can be used to obtain rich formation trajectories with varying curvatures between vehicles. By imposing adequate constraints on the motion of the virtual vehicles, the planner naturally guarantees the generation of valid formation trajectories, without requiring the parametrization of the space curve described by the leader. The trajectories are generated online and provided to a trajectory tracking controller specifically designed for quadrotor vehicles. Results of experimental tests are presented demonstrating the performance of the proposed solution for formation control of autonomous vehicles.

Keywords:Filtering, Linear parameter-varying systems, LMI's/BMI's/SOS's Abstract: This paper is concerned with the problem of H-infinity linear parameter-varying (LPV) filter design for discrete-time linear systems where the measurement of the scheduling parameters may be affected by additive and multiplicative uncertainties. By conveniently modeling the uncertainties and the time-varying parameters, new robust linear matrix inequality (LMI) conditions for the existence of a full order LPV filter assuring a prescribed H-infinity performance, irrespective of the uncertainties affecting the measures, are given. The design procedure can simultaneously handle time-invariant uncertainties and arbitrary time-varying parameters as well. The problem is solved through LMI relaxations based on homogeneous polynomial matrices of arbitrary degree. A numerical experiment illustrates the performance of the proposed LPV filter when compared to other filters obtained with methods from the literature.

Keywords:Linear parameter-varying systems Abstract: In this paper, the problem of designing a parameter-scheduled state-feedback controller is investigated. The main novelty and contribution of this paper is the extension of the classical regional pole placement problem, that will be referred to as shifting pole placement, to the design of parameter scheduled controller taking advantage of polytopes and LMIs properties. By introducing some parameters, or using existing ones, the controller can be designed in such a way that different values of these parameters imply different regions where the closed-loop poles are situated. The problem is analyzed in both linear time-invariant (LTI) and parameter-varying (LPV) cases, and some results obtained in simulation are shown so as to demonstrate the effectiveness of the proposed approach.

Keywords:Linear parameter-varying systems, H2/H-infinity methods, LMI's/BMI's/SOS's Abstract: A reduced-order gain-scheduling controller based on two time-varying parameters for the rejection of harmonic disturbances with time-varying frequencies is presented. The frequencies are harmonically related and assumed to be known. The control design results in a discrete-time controller with an order which is two times the number of frequency components of the multisine disturbance. Two gain-scheduling parameters are used independently of the number of harmonic components and a triangle is considered as the polytope, therefore the controller is obtained by interpolation between three controllers calculated for the vertices of the polytope. The resulting controller structure is therefore very simple. Experimental results on an active vibration control test bed are used to validate the controller.

Keywords:LMI's/BMI's/SOS's, Linear parameter-varying systems, Linear systems Abstract: In the framework of LPV and qLPV controller design one often encounter the problem of finding a maximal negative graph subspace of a parameter dependent non-singular indefinite matrix. For practical reason it is necessary that these subspaces depend continuously on the parameters. The paper provides an exhaustive condition for the existence of such a continuous solution.

Keywords:Linear parameter-varying systems, Observers for nonlinear systems, Robust control Abstract: This paper presents advances in the damping of container crane load swing via hoisting modulation based on linear parameter-varying (LPV) control techniques. We propose controllers based on constant, as well as parameter-dependent Lyapunov functions and formulate our problem in the linear fractional transformation (LFT) framework. The dynamics of a nonlinear observer are included into the generalized plant. Simulation and experimental results are compared to previous work using a polytopic LPV approach, as well as to earlier work based on the concept of resonant coupling control realized by a reduced normal form approach. The comparison indicates, that including the observer dynamics in the synthesis comes at the price of reduced performance, which is alleviated by the use of parameter-dependent Lyapunov functions. Furthermore, an a posteriori analysis verifies that the controller is robust against erroneously estimated scheduling signals and thus provides closed-loop guarantees for stability and performance for the new controller.

Keywords:Linear parameter-varying systems, Lyapunov methods, Filtering Abstract: In this paper, the problem of robust filter design for uncertain continuous-time systems is investigated in the context of finite time stability. The filter is obtained in order to guarantee that the augmented system is finite time stable. The system is considered time varying with the parameters modeled by a polytope. The design conditions obtained by means of Lyapunov functions are expressed as linear matrix inequalities. A complete order filter is obtained by the solution of a factibility problem. A numerical example is provided.

Keywords:Agents and autonomous systems, LMI's/BMI's/SOS's, Linear systems Abstract: This paper considers the robust design of sparse relative sensing networks subject to a given Hinf-performance constraint. The topology design considers heterogenous agents over weighted graphs. We develop a robust counterpart to the uncertain optimization problem and formulate the sparsity constraint via a convex l1-relaxation. We also demonstrate how this relaxation can be used to embed additional performance criteria, such as the maximization of the algebraic connectivity of the relative sensing network.

Keywords:Agents and autonomous systems, Stability of linear systems, Agents networks Abstract: This paper presents convergence bounds for discrete-time second-order multi-agent systems with undirected or directed communication graphs. As has been shown before, the convergence depends on the eigenvalues of the Laplace matrix of the communication graph. For each eigenvalue (or eigenvalue pair) analytic bounds for the parameter set are given to render the protocol for that eigenvalue pair stable. In addition it is shown examplarily, that for the case of normalized Laplacian, the stabilizing solution set for the whole topology is non-empty.

Keywords:Concensus control and estimation, Network analysis and control, Agents networks Abstract: We consider the problem of reaching consensus in a network of the first-order continuous-time agents with switching topology. The coupling gains are neither piecewise-ontinuous, nor separated from zero, nor symmetric, though the network topology is assumed to be undirected. The main result of the paper provides conditions on the network topology that are necessary and sufficient for reaching consensus.

Keywords:Agents and autonomous systems, Stability of nonlinear systems, Distributed control Abstract: The paper presents distributed control design to stabilize circular formations of steered particles in three-dimensional space. In formation, the particles are required to follow equal radius circular paths with common orientation, but not necessarily common center. The formation is given by specifying desired separations of the centers of the circular paths and desired relative headings. The information exchange between the particles is modeled by a directed graph which is assumed to have a spanning tree. Control design is based on a hierarchical approach utilizing a reduction principle for asymptotic stability of closed sets.

Keywords:Agents and autonomous systems, Delay systems, Stability of linear systems Abstract: In this paper the consensus problem for continuous time multi-agent systems in the presence of time-delay is addressed. A novel sufficient condition for the case of nonuniform non-differentiable time-varying delays with minimum value greater than zero and a method to compute an estimate of the convergence rate are given. Simulation examples are given to show the performance of the proposed method.

Keywords:Concensus control and estimation, Robust control, Decentralized control Abstract: We introduce the notions of H_infinity almost regulated synchronization and H_infinity almost formation for multi-agent systems subject to external disturbances and under directed interconnection structures. We assume that agents are linear, right-invertible and introspective with non-identical dynamics. The objective is to suppress the impact of disturbances on the synchronization error dynamics in terms of the H_infinity norm of the corresponding closed-loop transfer function. Inspired by the time-scale structure assignment techniques based on the singular perturbation theory, a family of observer-based protocols is introduced to achieve synchronization with any desired accuracy.

Keywords:Identification Abstract: The paper proposes a new approach for identifying linear dynamic errors-in-variables (EIV) models, whose input and output are affected by additive white noise. The method is based on a nonlinear system of equations consisting of part of the compensated normal equations and of a set of high order Yule-Walker equations. This system allows mapping the EIV identification problem into a quadratic eigenvalue problem that, in turn, can be mapped into a linear generalized eigenvalue problem. The system parameters are thus estimated without requiring the use of iterative identification algorithms. The effectiveness of the method has been tested by means of Monte Carlo simulations and compared with those of other EIV identification methods.

Keywords:Identification Abstract: In this paper, we apply an algebraic method to estimate the amplitudes, phases and frequencies of a biased and noisy sum of complex exponential sinusoidal signals. Let us stress that the obtained estimates are integrals of the noisy measured signal: these integrals act as time varying filters. Compared to usual approaches, our algebraic method provides a more robust estimation of these parameters within a fraction of the signal's period. We provide some computer simulations to demonstrate the efficiency of our method.

Keywords:Identification Abstract: A crucial issue in next generation many-core computing systems is the dynamic thermal control for run-time performance optimization. To this end, scalable, compact and effective thermal models are essential. In this paper, we present an algorithm based on the Frisch scheme to obtain identification of distributed core-centric interacting models, dealing with very noisy temperature measurements and high process noises. We apply the proposed solution to an Intel's Single-chip-Cloud-Computer (SCC), a many-core prototype with 48 cores.

Keywords:Identification, Linear parameter-varying systems, Optimization algorithms Abstract: This paper presents a comparison of two techniques dedicated to the identification of LPV systems by using local experiments only. Such an approach can be justified by the fact that, in many practical cases, exciting the scheduling variables persistently is not conceivable for safety/economic reasons. According to the prior information available on the system, a black-box and a gray-box model-based technique are described and compared through a simulation example. More precisely, a new version of the algorithm suggested in [1] is compared with a gray-box model-based technique consisting in interpolating local re-structured LTI state-space models, whose basis coherence is ensured thanks to prior knowledge about the system to identify. This contribution shows that prior information can be really helpful when the problem of coherent basis selection arises.

Keywords:Identification, Linear time-varying systems Abstract: This paper suggests an extended recursive least squares algorithm for simultaneous identification of an unknown time delay and dynamic parameters of discrete-time varying delay systems. The basic idea is to obtain a new formulations allowing to admit the unknown time varying delay in the parameter vector. The recursive least-squares method is then used to deal with the identification problem. A simulation study is included to illustrate the merit of our algorithm.

Keywords:Identification, Linear systems, Linear time-varying systems Abstract: This paper is concerned with identifiability of an underlying high frequency multivariate stable singular AR system from mixed frequency observations. Such problems arise for instance in economics when some variables are observed monthly whereas others are observed quarterly. In particular, this paper studies stable singular AR systems where the covariance matrix associated with the vector obtained by stacking observation vector, y_t, and its lags from the first lag to the p-th one (p is the order of the AR system), is also singular. To deal with this, it is assumed that the column degrees of the associated polynomial matrix are known. We consider first that there are given nonzero unequal column degrees and we show generic identifiability of the system and noise parameters. Then we extend the results to allow zero column degrees corresponding to fast components. In this case, we first show generic identifiability of the subsystem of the components with nonzero column degree. Then we show how to obtain those components of the parameter matrices of the components corresponding to zero column degree by regression.

Keywords:Fault diagnosis, Fault detection and identification, Stochastic systems Abstract: This paper establishes optimal/suboptimal active fault detection and diagnosis (FDD) methods in which semidefinite programming relaxation is used and the optimality criteria are information theoretic measures of the statistical distance between probability distributions. The design problems are formulated as optimizations in which an optimal sequence of inputs within a prediction horizon is computed for maximizing the statistical discrimination of different models of fault scenarios. Three different measures for the degree of statistical distinguishability between two hypothesized stochastic dynamical system models are considered and their mathematical properties that are related to Bayesian hypothesis tests are studied. The resulting input design problems are non-convex and we propose associated convex relaxation methods that can be solved in polynomial time using interior point methods. In addition, an upper bound on the sub-optimality of the proposed convex relaxation is presented for the case when there is only the input amplitude constraint, and randomized algorithms are presented to compute a suboptimal solution from an optimal solution of the convex relaxation problem. Numerical simulations with an aircraft model are provided to illustrate and demonstrate the presented methods of optimal input design for FDD.

Keywords:Fault diagnosis, Fault estimation, Stochastic systems Abstract: This paper proposes optimization-based active fault detection and diagnosis (FDD) methods. An optimal input sequence is computed for maximizing discrimination between system models of fault scenarios in a statistical sense. Two different measures quantifying the degree of distinguishability between two stochastic LTI system models are considered, and their geometric properties are investigated. Their connection to the generalized likelihood ratio tests are also presented. Constrained open- and closed-loop feedback input design methods using model-based prediction are presented. Constraints on the predicted controlled output trajectory are imposed for ensuring operational safety as well as the input constraints that correspond to hardware limitations. Receding horizon method is used to implement the computed inputs.

Keywords:Fault diagnosis, Observers for nonlinear systems, Adaptive systems Abstract: A bank of nonlinear adaptive observers is used for fault diagnosis in oil and gas drilling where managed pressure drilling (MPD) is applied. The particular fault considered is formation of a pack-off, causing increased friction in one part of the annulus. The process model is a simplified hydraulics model with a Newtonian fluid. All states in the model are assumed measurable, an assumption based on planned implementation of the wired drill pipe measurement technology. A fault detection observer is used to detect that a pack-off is being formed somewhere in the annulus. Then a set of fault isolation and approximation observers, one for each possible fault, is used to isolate the location of the pack-off and estimating its magnitude. Isolation is done by using residuals of annular friction estimation. The method for fault diagnosis is illustrated in a simulation study.

Keywords:Fault diagnosis, Large-scale systems, Fault detection and identification Abstract: This paper presents the design of a methodology for detecting and isolating multiple sensor faults in large-scale interconnected nonlinear systems. For each of the interconnected subsystems, we design a local sensor fault diagnosis (LSFD) agent responsible for multiple sensor fault detection and isolation in the local sensor set. The multiple sensor fault detection is realized through a bank of modules, monitoring smaller groups of sensors that belong to the local sensor set. The detection of faults in sensor groups is conducted using robust analytical redundancy relations, formulated by structured residuals and adaptive thresholds. The isolation of multiple faulty sensors in the local sensor set is realized by integrating the decisions of the LSFD agent's modules and applying a reasoning-based combinatorial decision logic. The simulation example of an automated highway system is used to illustrate the application of the multiple SFDI methodology.

Keywords:Fault diagnosis, Markov processes, Computational methods Abstract: Most of the existing methods for qualitative trend analysis are based on discriminative models. A disadvantage of such models is that many heuristic rules or local search methods are needed. Recently, an effort has been made to develop a globally optimal method for qualitative trend analysis. This method is based on a generative (rather than discriminative) model and has shown to lead to excellent performance. However, this method comes at an extreme computational demand which renders the methods unlikely for on-line application. In this work, an alternative method, while still generative in nature, is proposed which is shown to deliver the same performance while reducing the computational demand considerably.

Keywords:Fault diagnosis, Fault detection and identification Abstract: Isolating fault variables is a crucial step to provide the information that which variables are responsible for the fault for diagnosing the root causes of a process fault. In chemical processes, process faults rarely show a random behavior; on the contrary, they will be propagated to varying variables due to the actions of the process controllers. During the evolution of a fault, the task of isolating faulty variables needs to be concerned with the faulty variables decided in the previous data; in addition, the current decisions should influence the isolation results for the next sample when the fault is constantly occurring. In the presented work, an unsupervised data-driven fault isolation method was developed based on Bayesian decision theory. The proposed approach successfully located the faulty variables that were individually responsible for the simultaneous occurrence of multiple sensor faults and a process fault.

Keywords:Automotive, Identification Abstract: This paper deals with the design of a multiple model based controller for the nitrogen oxide emissions (NOx), from vehicles using the selective catalyst as an aftertreatment system. The selective catalyst reduction (SCR) system is nonlinear, since the chemical reactions involved are highly depending on the operating points. Local linear models were used for identification. Local internal controllers are integrated into a global controller. A Bayesian approach is used to mix the local output of the controllers. A detailed simulator is used for the multiple model identification and testing the controller. For validation, experimental data based on a standard transient test developed for Euro VI testing are used in the simulator. Results obtained for this control approach are compared to one model controller.

Keywords:Automotive, Modeling Abstract: A model for a vehicle equipped with a multimode combustion engine is formulated and calibrated to experiments. A study is performed for the FTP-75 driving cycle about the influence of the mode switch strategy on the engine operation and fuel consumption, using simulation results and driving cycle measurements. It is found that the fuel penalty for mode transitions cancels a significant part of the theoretical benefits of advanced combustion modes. A smoothing strategy, where a mode switch is delayed, is introduced and it is shown that, by computing the optimal wait time, the negative influence of mode transitions on the overall efficiency can be reduced.

Keywords:Automotive, Modeling, Identification Abstract: Internal combustion engine test benches allow to simulate the operation of an engine under various conditions and are essential in engine development in the automotive industry. Models of such test benches are often used in the design and improvement of test bench controls and to simulate their behavior. Therefore, the paper summarizes a modeling procedure based on a simple model structure. In particular, the individual components of a test bench are described and their models are combined. A torque observer is used to compensate the lack of torque measurements. Finally, a model for a test bench equipped with a heavy duty engine is determined and validated with measurements.

Keywords:Automotive, Predictive control for linear systems, Observers for nonlinear systems Abstract: In this paper, a control-oriented model of a combustion-heating system for vehicles such as buses, coaches and trucks is developed. Based on this model, a novel model predictive on-off strategy is proposed for the control of the combustion-heating system. Experiments are carried out to obtain a fair comparison of the predictive on-off controller with a classical on-off controller. The classical on-off controller and the predictive on-off controller are evaluated with respect to fuel economy, reduction in the emission of pollutants and the number of on-off switching cycles of the combustion valve connected to the heater. A discrete-time Extended Kalman Filter is employed for the estimation of state variables, heat losses and the volumetric flow. Experimental results show that the predictive on-off control strategy leads to a superior performance in terms of fuel economy and switching action of the valve as compared to the classical on-off controller.

Keywords:Feedback linearization, Automotive, Linear time-varying systems Abstract: The goal is to develop a controller for a common rail injection system where the calibration process for the implementation is systematic and simpler. A 0D nonlinear model of the common rail system is designed. The common rail model contains strong nonlinearities which might be hard to handle from the control point of view. In order to overcome this constraint, an input-to-state linearization is applied to the common rail nonlinear model. This procedure yields with a virtual linear system, where two optimal Linear Quadratic Regulator LQR strategies are applied. Very good results are obtained with the LQR, the calibration process is dramatically simplified and the controller stability is ensured.

Keywords:Switched systems, Automotive, Identification for hybrid systems Abstract: Nitrogen oxides (NOx) emission control is a critical task of engine control as far as raw emissions and aftertreat- ment is concerned. Hardware NOx sensor are now available, but they still have several limitations, starting from their costs. Against this background, a lot of work both inside companies and in the academy has been done to develop virtual sensors for these emissions. In this paper, we propose a minimum-complexity model in the form of a piecewise affine model, and show that its performance is comparable to more complex models and better than conventional sensors if dynamic response is concerned.

Keywords:Cooperative autonomous systems, Stability of nonlinear systems, Optimization Abstract: Demand side management will be an important tool for maintaining a balanced electrical grid in the future, when the penetration of volatile resources, such as wind and solar energy increases. Recent research focuses on two different management approaches, namely direct consumer control by an external third party, and indirect consumer control through incentives and price signals. In this work we present a simple formulation of indirect control, where the behavior of each consumer, is governed by local optimization of energy consumption. The local optimization accounts for both cost of energy and distribution losses, as well as any discomfort incurred by consumers from any shift in energy consumption. Our work will illustrate that in the simplest formulation of indirect control, the stability is greatly affected of both the behavior of consumers, and the number of consumers to include. We will show how instability is related to the local optimization problem of the consumer, and the information made available to him.

Keywords:Hybrid systems, Stochastic control, Energy systems Abstract: Microgrids are subsystems of the distribution grid which comprises generation capacities, storage devices and controllable loads, operating as a single controllable system that can operate either connected or isolated from the utility grid. In this work, microgrid management system is developed in a stochastic framework. It is seen as a constraint-based system that employs forecasts and stochastic techniques to manage microgrid operations. Uncertainties due to fluctuating demand and generation from renewable energy sources are taken into account and a two-stage stochastic programming approach is applied to efficiently optimize microgrid operations while satisfying a time-varying request and operation constraints. Mathematically, the stochastic optimization problem is stated as a mixed-integer linear programming problem, which is solved in an efficient way by using commercial solvers. The stochastic problem is incorporated in a Model Predictive Control (MPC) scheme to further compensate the uncertainty though the feedback mechanism. Simulations show the effective performance of the proposed approach.

Keywords:Energy systems, Emerging control applications, Fuzzy systems Abstract: In model based control approaches for the dynamic operation of renewable-energy based microgrid, an accurate demand forecast is crucial. However, the high level of uncertainties in the system and non-linearities make the task of prediction not easy. In this context, we propose the use of a stable Takagi & Sugeno (T&S) fuzzy model to perform the demand forecasting in a real-life microgrid located in Huatacondo, Chile. Based on real-data from the microgrid, located in northern Chile, the T&S fuzzy model was identified and compared with an adaptive neural network, showing the T&S fuzzy model better open-loop prediction capabilities. To increase the prediction capability, an analysis of the amount of historical data needed, and the frequency required for training purposes was also done. For the case study, it is suggested to use a large amount of data rather than increasing the training frequency.

Keywords:Energy systems, Optimal control, Model/Controller reduction Abstract: This paper is concerned with optimal energy management of micro-grids. The goal is to show that the problem of minimizing the operating costs of a micro-grid by coordinating and scheduling its components can be formulated as a constrained optimal control problem for a stochastic hybrid system. This, in turn can be addressed through the Dynamic Programming (DP) approach, and the resulting DP equations solved through approximate DP techniques. A simple case study of a building cooling system with two chillers serving a cooling load is presented to this purpose.

Keywords:Game theoretical methods, Electrical power systems, Distributed control Abstract: Smart grids are a novel paradigm for energy distribution, where instead of the traditional directed flow from a producer to the consumers, several micro-generators are spread throughout the network. We focus on the problem of coordinating the active power injected into the grid among the micro-generators. Each of them aims at injecting the maximum amount of power, satisfying some operative constraint such as voltage boundaries, but a tradeoff must be found among these conflicting objectives. First, we characterize the active power increment region, i.e., the set of all the increments of injected power that, depending on the grid state, satisfy the voltage boundary. Based on this finding, we frame the problem within game theory and propose a distributed approach that achieves a fair share of the active power injection, while at the same time satisfying the voltage boundary.

Keywords:Electrical power systems, Energy systems, Stability of nonlinear systems Abstract: Voltage stability is of essential importance for power grids. The emergence of distributed energy generators, controllable loads, and local-area energy storage capabilities have introduced new scenarios for distribution networks inwhich classical frameworks for voltage stability may be inadequate. This paper introduces a control-theoretic framework for studying voltage stability and its robustness, as well as optimal power management in distribution systems composed of networked microgrids. The framework involves descriptions of the loads and generators by nonlinear state space models and the network connections by a set of topology-based algebraic equations. The integration of the combined system leads to a general nonlinear state space model for the microgrid systems. Simplified microgrids are used to illustrate the concepts.

Keywords:Predictive control for nonlinear systems Abstract: In this paper, we propose an economic model predictive control (MPC) framework with a self-tuning terminal weight, which builds on a recently proposed MPC algorithm with a generalized terminal state constraint. First, given a general time-varying terminal weight, we derive an upper bound on the closed-loop average performance which depends on the limit value of the predicted terminal state. After that, we derive conditions for a self-tuning terminal weight such that bounds for this limit value can be obtained. Finally, we propose several update rules for the self-tuning terminal weight and analyze their respective properties. We illustrate our findings with several examples.

Keywords:Optimal control, Robust control, Predictive control for nonlinear systems Abstract: Motivated by the passivity-based nonlinear model predictive control (NMPC) scheme reported in [1], in this paper, we propose a robust stabilizing output feedback NMPC scheme by using passivity and disspativity. Model discrepancy between the nominal model and the real system is characterized by comparing the outputs for the same excitation function, and with this kind of characterization, we are able to compare the supply rate between the nominal model and the real system based on their passivity indices. Then, by introducing specific stabilizing constraint based on the passivity indices of the nominal model into the MPC, we show that our proposed NMPC scheme can stabilize the real system to be controlled.

Keywords:Predictive control for nonlinear systems, Feedback linearization, Aerospace Abstract: Model predictive control (MPC) is one of the most popular advanced control techniques and is used widely in industry. The main drawback with MPC is that it is fairly computationally expensive and this has so far limited its practical use for nonlinear systems.

To reduce the computational burden of nonlinear MPC, Feedback Linearization together with linear MPC has been used successfully to control nonlinear systems. The main drawback is that this results in an optimization problem with nonlinear constraints on the control signal.

In this paper we propose a method to handle the nonlinear constraints that arises using a set of dynamically generated local inner polytopic approximations. The main benefits of the proposed method is guaranteed recursive feasibility and convergence.

Keywords:Predictive control for nonlinear systems, Model/Controller reduction, Chemical process control Abstract: We consider a class of process systems with significant energy recovery. Extending our previous results concerning the two time scale dynamics of such systems, we demonstrate that the fast component of their dynamics is asymptotically stable in most physically-relevant cases. Using this result, we develop a composite controller design, consisting of a linear control system for the fast dynamics and a MISO nonlinear model predictive controller for the slow dynamics, and demonstrate that it guarantees exponential stability for the overall system. Subsequently, we establish a parallel between this approach and economic model predictive control, and show its implications in optimal energy management. We illustrate our theoretical developments with a simulation case study.

Keywords:Predictive control for nonlinear systems, Uncertain systems, Constrained control Abstract: In this paper, Incremental Input-to-State Stability is studied as a system theoretic framework to address the challenges of robust nonlinear model predictive control. In the first part of the paper, a Lyapunov framework for Incremental Input-to-State Stability of nonlinear discrete-time dynamical systems is established. In the second part, Incremental Input-to-State Stability is shown to lead to an efficient MPC method for disturbed nonlinear systems. Based on the Incremental Input-to-State Stability Lyapunov function, a tightening of the constraints is proposed. Satisfaction of the tightened constraints can be guaranteed under the disturbances. By this concept, a robust nonlinear model predictive control problem is handled and the effectiveness is shown through an example from the literature.

Keywords:Predictive control for nonlinear systems, Modeling, Manufacturing processes Abstract: The Swedish nuclear waste will be stored in copper canisters and kept isolated deep under ground for more than 100,000 years. To ensure reliable sealing of the canisters, friction stir welding is used. To repetitively produce high quality welds, it is vital to use automatic control of the process. This paper introduces a nonlinear model predictive controller for regulating both plunge depth and stir zone temperature, which has not been presented in literature before. Further, a nonlinear process model has been developed and used to evaluate the controller in simulations of the closed loop system. The controller is compared to a decentralized solution, and simulation results indicate that it is possible to achieve higher control performance using the nonlinear model predictive controller.

Keywords:Quantum control, Distributed parameter systems, Nonlinear system theory Abstract: The aim of this paper is to provide a short introduction to modern issues in the control of infinite dimensional closed quantum systems, driven by the bilinear Schrodinger equation.

The first part is a quick presentation of some of the numerous recent developments in the fields. This short summary is intended to demonstrate the variety of tools and approaches used by various teams in the last decade. In a second part, we present four examples of bilinear closed quantum systems. These examples were extensively studied and may be used as a convenient and efficient test bench for new conjectures. Finally, we list some open questions, both of theoretical and practical interest.

Keywords:Delay systems, Distributed parameter systems, Linear systems Abstract: In this paper, a parametric approach for state feedback controllers for a class of linear infinite-dimensional systems is presented. Therein, besides the closed-loop eigenvalues, the corresponding parameter vectors are introduced as design parameters. This allows not only to assign finitely many eigenvalues, but also the corresponding eigenvectors. The presented approach is applied to solve a partial eigenstructure assignment problem for linear time-delay systems with point-delays. An example for the usefulness of the proposed design method is then given by a partial input-output decoupling of a simple time-delay system.

Univ. of Bristol, Department of Mechanical Engineering

Keywords:Distributed parameter systems, Flexible structures, Robust control Abstract: In this study we consider the robust control of an inclined cable modelled using partial differential equation and subjected to external disturbances. This paper focuses on the construction of a standard linear infinite dimensional state space system and an H-infinity feedback control with full observation of the state.

Keywords:Differential algebraic systems, Distributed parameter systems, Stability of linear systems Abstract: The main contribution of this paper is the generalisation of well-known energy-based control techniques (i.e., energy-balancing passivity-based control and passivity-based control with state modulated source), to the case in which the plant is a port-Hamiltonian system in implicit form. A typical situation is when (part of) the system is obtained from the spatial discretization of an infinite dimensional port-Hamiltonian system: in this case, the dynamics is not given in standard input-state-output form, but as a set of DAEs. Consequently, the control by energy-shaping has to be extended to deal with dynamical systems with constraints. The general methodology is discussed with the help of a simple but illustrative example, i.e. a transmission line interconnected with an RLC circuit.

Keywords:Distributed parameter systems, Model/Controller reduction, Linear systems Abstract: Finite-dimensional approximations of partial differential equations are used not only for simulation, but also for controller design. Modal truncation and numerical approximation are common practical methods for approximating distributed parameter systems. The modal approximation preserves the exact, low-order poles of the original system. However, the zeros of modal approximations may differ significantly from those of the original distributed parameter system. In particular, right half-plane zeros, which are not present in the original infinite-dimensional model, may appear in modal truncations. In this paper we consider a boundary control system and propose a moment matching based approximation which preserves a prescribed set of zeros. To illustrate the advantages of the method, we consider its application to the heat equation with Neumann boundary control at the right end (HENBCR). Although the modal approximation provides good error bounds for the HENBCR, it contains non-minimum phase zeros which lead to erroneous predictions. The moment matching approach sketched in this paper yields an approximation of the HENBCR with minimum phase zeros only. We consider that the numerical example is very interesting and convincing for the reader. Further theoretical analysis will be addressed in the full paper.

Keywords:Quantum control, Distributed parameter systems Abstract: In this paper we study the so-called spin-boson system, namely a spin-1/2 particle in interaction with a distinguished mode of a quantized bosonic field. We control the system via an external field acting on the bosonic part.

Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost every value of the interaction parameter.

Keywords:Observers for nonlinear systems, Delay systems, Observers for linear systems Abstract: The estimation problem for uncertain time-delay systems is addressed. A design method of reduced-order interval observers is proposed. The observer estimates the set of admissible values (the interval) for the state at each instant of time. The cases of known fixed delays and uncertain time-varying delays are analyzed. The proposed approach can be applied to linear time-delay systems and nonlinear time-delay systems in the output canonical form. The framework efficiency is demonstrated on examples of nonlinear systems.

Keywords:Hybrid systems, Observers for nonlinear systems, Chaotic systems Abstract: Dynamical behaviors in a recently proposed observer for linear time-invariant systems under intrinsic pulse-modulated feedback are studied. A special case of scalar continuous dynamics is considered as it is not covered by the previously presented mathematical analysis. Notably, the lowest non-trivial differential order of the continuous part of the plant results in a more complex dynamics of the observer. In fact, the convergence of the observer becomes dependent on the observer initialization, which phenomenon does not exist in the case of the second and higher order continuous dynamics. As an alternative to the static gain observer, an integral feedback observer is suggested that exhibits global convergence for certain values of the observer gain and types of the periodic solution in the observed plant. Extensive bifurcation analysis is though necessary to select a proper observer gain.

Keywords:Filtering, Aerospace Abstract: A novel adaptive unscented Kalman filter (AUKF) based estimation algorithm is proposed for a 3U Cubsat. This small satellite employs a three axis magnetometer and three MEMS gyroscopes as well as three magnetic torque rods and one reaction wheel on the pitch axis. Unlike the existing UKF, in this paper, an n+1 sigma set is used to estimate the nanosatellite attitude instead of 2n+1 sigma points as in a conventional UKF. Numerical Simulation results validate the performance of the proposed adaptive Kalman filter. There is no need for linearization of the nonlinear dynamics of the system. The estimated result tracks satellite attitude during the damping and stable control stages. Euler angles, gyro bias, and angular velocity of the satellite are estimated using this proposed AUKF with good convergence time and estimation accuracy.

Keywords:Observers for nonlinear systems, Stochastic systems, Nonlinear system theory Abstract: This paper applies contraction theory to establish sufficient conditions for contraction, hence, exponential convergence of the unscented Kalman-Bucy Filter. It follows that regions of contraction can subsequently be defined, given such sufficient conditions. Both state, and measurement models are It^o type stochastic differential equations. By employing a virtual/actual system framework, a special relation is established between sigma-point dynamics, and observed process states, with respect to contraction and convergence. The proposed theory is illustrated on an isothermal, non-linear CSTR process.

Keywords:Observers for nonlinear systems, Lyapunov methods Abstract: This paper proposes a state observer with a cascade structure for a class of nonlinear systems in the presence of delayed output measurements. The first system in the cascade allows to estimate the delayed state while each of the remaining ones is a predictor. Each predictor estimates the state of the preceding one with a prediction horizon equal to a fraction of the time delay in such a way that the state of the last predictor is an estimate of the system actual state. The design of the observer is achieved by assuming a set of conditions under which the exponential convergence of the estimation error to zero is established, namely the system is uniformly observable for any any input and its nonlinearities are globally Lipschitz. Of particular interest, it is shown that the number of the systems in the cascade depends on the magnitudes of the considered delay and the Lipschitz constant. The performance of the proposed observer and its main properties are compared with those of two existing observers through a typical bioreactor model.

Keywords:Observers for nonlinear systems, Lyapunov methods Abstract: In this paper, we investigate the possibility of designing an observer for a class of continuous-time dynamical systems with non-uniformly sampled measurements. More specifically, we propose an observer with a time varying gain witch converges exponentially under some conditions on the sampling partition diameter. The proposed observer is an impulsive system since it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates. As it is customarily done in the literature, we show that such an impulsive system can be split into two subsystems and be put under the form of a hybrid system which is designed using a continuous-time observer together with an inter-sample output predictor. Simulations results involving a typical bioreactor are given to show the effectiveness of the proposed observer

Keywords:Switched systems Abstract: In this paper we extend the result by Shorten and Narendra on common quadratic Lyapunov functions for pairs of matrices in companion form. Specifically, we show that their result extends to more general matrix pairs provided that an associated transfer function matrix is symmetric. Examples are given to illustrate the usefulness of this result.

Keywords:Switched systems, Algebraic/geometric methods, Stability of linear systems Abstract: It is well-known that disturbances with different features (i.e., inaccessible, measurable, or previewed disturbances) must be handled with the appropriate compensation schemes: namely, those which better exploit the available information. In particular, this work is focused on rejection of disturbances accessible for measurement in continuous-time linear switching systems, with the requirement that the compensated system be quadratically stable under arbitrary switching. A dynamic feedforward switching compensator is designed on the assumption that the plant be quadratically stable under arbitrary switching. This assumption can be relaxed to quadratic stabilizability by linear state feedback and by linear output injection, provided that a measurement dynamic feedback stabilizer is also devised. The proposed techniques apply to linear switching systems whose modes may be either left-invertible or not. The methodology adopted is based on the use of the geometric approach enhanced with stability notions which are typically considered in linear switching systems.

Keywords:Switched systems, Differential algebraic systems, Stability of hybrid systems Abstract: Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switched ordinary differential equations. In this paper the averaging technique is shown to be useful also for the analysis of switched systems whose modes are represented by means of differential algebraic equations (DAEs). An approximation result is derived for a simple but representative homogenous switched DAE with periodic switching signals and two modes. Simulations based on a simple electrical circuit model illustrate the theoretical result.

Keywords:Switched systems, Stability of linear systems, Stability of hybrid systems Abstract: Given a single-input continuous-time positive system, described by a pair (A,b), with A a diagonal matrix, we investigate under what conditions there exist state-feedback laws u(t) = c'x(t) that make the resulting controlled system positive and asymptotically stable, namely A+b c' Metzler and Hurwitz. In the second part of the paper we assume that the state-space model switches among different state-feedback laws c_i, i=1,2,...,p, each of them ensuring the positivity, and show that the asymptotic stability of the switched system is equivalent to the asymptotic stability of all the subsystems, while its stabilizability is equivalent to the existence of an asymptotically stable subsystem.

Keywords:Switched systems, Optimal control, Linear time-varying systems Abstract: This paper presents a method to compute an epsilon-optimal solution of the control problem of switched linear systems. A difficulty that emerges in the evalution of the optimal solution is that the cardinality of the solution set increases exponentially as long as the time-horizon increases linearly, which turns the problem intractable when the horizon is sufficiently large. We propose a numerical method to overcome such difficulty, in the sense that our approach allows the evalution of epsilon-optimal solutions with corresponding sets that do not increase exponentially.

Keywords:Switched systems, Observers for linear systems Abstract: In this paper, we study a switching signal estimation problem for continuous time switched linear control systems with measurement noise. Inspired by the work of (Battistelli,2011), we first propose a generalized minimum distance criterion to estimate the active mode of the plant with inputs. Then we propose an implementable on-line robust switching signal estimation algorithm to detect the switching time with guaranteed precision, where some update condition and threshold condition are checked all the time. Under the update and threshold conditions, we detect the switching time within a predetermined time interval after the switching occurred.

Keywords:Nonlinear system theory, Algebraic/geometric methods, Lyapunov methods Abstract: The paper discusses stabilization of nonlinear discrete-time dynamics exhibiting strict feedforward structures. An iterative design procedure is proposed which makes use of average passivity based controllers. This concept has been recently introduced by the authors because the usual definition in unsuitable in the absence of direct input-output link. Due to the triangular structure of strict feedforward dynamics, it is possible, at each step of the procedure and through coordinates change, to reset the problem as the one of average passivity based controller design. The complete controller is derived at the last step and a Lyapunov function is constructed. An example concludes the paper.

Keywords:Stability of nonlinear systems, Robust control, LMI's/BMI's/SOS's Abstract: This paper proposes an algorithm for stability analysis of systems containing slope-restricted nonlinearities using high-order Zames-Falb multipliers. The main innovation in this paper is the use of a new congruence transformation which enables multipliers of twice the order of the linear part of the system to be used in a linear-matrix-inequality (LMI) framework for stability analysis. Although the use of such high-order multipliers increases the algorithms computational requirements, various numerical examples show that the resulting stability bounds are sometimes less conservative than using other similar approaches.

Keywords:Stability of nonlinear systems, Lyapunov methods, Discrete event systems Abstract: Incremental stability is a property of dynamical and control systems, requiring the stability and convergence of trajectories with respect to each other, rather than with respect to an equilibrium point or a particular trajectory. Most design techniques providing controllers rendering control systems incrementally stable have two main drawbacks: they can only be applied to control systems in parametric-strict-feedback or strict-feedback form, and they require the control systems to be smooth. In this paper, we propose a controller design technique that is applicable to larger classes of control systems, including a class of non-smooth control systems. Moreover, we propose a recursive way of constructing incremental Lyapunov functions which have been identified as a key tool enabling the construction of finite abstractions of nonlinear control systems. The effectiveness of the proposed results in this paper is illustrated by synthesizing a controller rendering a non-smooth control system incrementally stable as well as constructing its finite abstraction, using the computed incremental Lyapunov function. Finally, using the constructed finite abstraction, we synthesize another controller for the incrementally stable closed-loop system enforcing the satisfaction of logic specifications, difficult (or even impossible) to enforce using conventional techniques.

Keywords:Nonlinear system theory, Stability of nonlinear systems Abstract: The notion of geometric homogeneity is extended for differential inclusions. This kind of homogeneity provides the most advanced coordinate-free framework for analysis and synthesis of nonlinear discontinuous systems. Theorem of L. Rosier on a homogeneous Lyapunov function existence for homogeneous differential inclusions is presented. An extension of the result of Bhat and Bernstein about the global asymptotic stability of a system admitting a strictly positively invariant compact set is also proved.

Keywords:Nonlinear system theory, Lyapunov methods, Stability of nonlinear systems Abstract: In this paper we present a sufficient condition for continuity of Lyapunov exponents of discrete time-varying linear system. Basing on the result we show that Lyapunov exponents of time-invariant systems depend continuously on the time-varying perturbations.

Keywords:Nonlinear system theory, Lyapunov methods, Complex systems Abstract: This paper investigates the bifurcation phenomenon of fractional-order discrete-time systems and proposes the nonlinear control to synchronize two fractional-order discrete-time systems. By taking a finite truncation, fractional-order discrete-time chaotic systems are constructed. Chaotic phenomenon is also determined by the fractional order. By adjusting the fractional-order appropriately, the chaotic areas can be controlled. The synchronization control is designed for the same and different fractional-orders in the drive and response systems. Finally, the bifurcation phenomenon and synchronization of fractional-order Logistic system are studied. The proposed method can be extended to synchronize other fractional-order discrete-time systems.

Keywords:Optimal control, Emerging control theory, Computational methods Abstract: In this article we introduce the use of recently developed min/max-plus techniques in order to solve the optimal attitude estimation problem in filtering for nonlinear systems on the special orthogonal (SO(3)) group. This work helps synthesize deterministic filters for nonlinear systems -- i.e. optimal filters which estimate the system state using a related optimal control problem. The technique indicated herein is validated using a set of optimal attitude estimation example problems on SO(3).

Keywords:Optimal control, Optimization algorithms, Switched systems Abstract: Max-plus based methods have been recently explored for solution of first-order Hamilton-Jacobi-Bellman equations by several authors. In particular, McEneaney's curse-of-dimensionality free method applies to the equations where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms. In previous works of McEneaney and Kluberg, the approximation error of the method was shown to be O(1/(Ntau))+O(sqrt{tau}) where tau is the time discretization step and N is the number of iterations. Here we use a recently established contraction result of the indefinite Riccati flow in Thompson's metric to show that under different technical assumptions, still covering an important class of problems, the total error incorporating a pruning procedure of error order tau^2 is O(e^{-alpha Ntau})+O(tau) for some alpha>0 related to the contraction rate of the indefinite Riccati flow.

Keywords:Computational methods, Nonlinear system theory, Optimal control Abstract: Nonlinear L2-gain is a generalization of the well-known finite L2-gain robust stability property for nonlinear systems. Computation of tight performance bounds associated with this nonlinear L2-gain property is key to avoiding conservatism in its application, for example in small-gain based design. In previous work, a number of max-plus eigenvector methods have been proposed to facilitate this computation. Those methods have each employed quadratic basis functions, which have been shown to lead to a specific computational issue concerning continuity of the associated Hamiltonian. In this paper, an alternative piecewise affine-quadratic basis is proposed that allows the development of a refined max-plus eigenvector method that avoids this computational issue.

Keywords:Computational methods, Optimal control, Optimization algorithms Abstract: This paper studies a class of linear regulator problem where the terminal payoff function is not necessarily quadratic. The value function for this problem is generally not quadratic and thus it can not be reduced to solving the corresponding matrix Riccati equation as for the standard linear quadratic regulator (LQR) problem. The computational method of direct iteration using the dynamic programming equations is computationally expensive. In this paper, a new computational method based on max-plus techniques is developed for this problem which is demonstrated to be more efficient and more accurate. In particular, three max-plus fundamental solutions are obtained which can be used as the kernel of max-plus integration with respect to the max-plus dual of the terminal payoff to generate the value function of the linear regulator problem.

Keywords:LMI's/BMI's/SOS's, Optimal control, Emerging control applications Abstract: We consider the problem of certifying an inequality of the form f(x)geq 0, forall xin K, where f is a multivariate transcendental function, and K is a compact semi-algebraic set. We introduce a certification method, combining semi-algebraic optimization and max-plus approximation. We assume that f is given by a syntaxic tree, the constituents of which involve semi-algebraic operations as well as some transcendental functions like cos, sin, exp, etc. We bound some of these constituents by suprema or infima of quadratic forms (max-plus approximation method, initially introduced in optimal control), leading to semi-algebraic optimization problems which we solve by semi-definite relaxations. The max-plus approximation is iteratively refined and combined with branch and bound techniques to reduce the relaxation gap. Illustrative examples of application of this algorithm are provided, explaining how we solved tight inequalities issued from the Flyspeck project (one of the main purposes of which is to certify numerical inequalities used in the proof of the Kepler conjecture by Thomas Hales).

Keywords:Optimization Abstract: In the paper we revisit some known remarkable formulas and their idempotent versions highlighting the role of functional spaces where the analogues take place and we discuss the different roles of R_min and R_max. More precisely, we focus on the space where the analogue of the Fourier transform takes place, the Legendre transform in R_min and the concave conjugate transform in R_max, then we give the analogues of some classical theorems.

Keywords:Adaptive systems, Adaptive control, Communication networks Abstract: Power control in mobile communications is an adaptive control system which functions routinely without direct human intervention. In this paper we examine the cost in terms of power usage of the one-parameter system identification problem of estimating the signal-to-noise ratio and thereby setting subsequent transmissions at the appropriate power level to accommodate the error detection and recovery. This is performed with an explicit formulation of the density function of the signal-to-noise ratio estimate and its dependence on the number of training samples used in this phase - it is a non-central chi^2 density if the noise power is known, else it is F-distributed. The objective is to develop a total cost function based on transmission power under which the price paid for adaptation becomes apparent. Our example is based on GSM mobile telephony systems and is part of a broader study into the costs associated with adaptation.

Keywords:Agents networks, Communication networks, Control over networks Abstract: Localization is a fundamental task for sensor networks. Traditional network localization approaches allow to obtain localized networks requiring the nodes to be at least tri-connected (in 2D), i.e., the communication graph needs to be globally rigid. In this paper we exploit, besides the information on the neighbors sensed by each robot/sensor, also the information about the lack of communication among nodes. The result is a framework where the nodes need to be at least bi-connected and the communication graph has to be rigid. This is possible considering a novel typology of link, namely Shadow Edge, that accounts for the lack of communication among nodes and allows to reduce the uncertainty associated to the position of the nodes.

Keywords:Autonomous systems, Agents and autonomous systems, Cooperative control Abstract: This paper presents a distributed algorithm for solving a linear algebraic equation of the form Ax=b where A is an ntimes n nonsingular matrix and b is an n-vector. The equation is solved by a network of n agents assuming that each agent knows exactly one distinct row of the partitioned matrix matt{A&b}, the current estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate of A^{-1}b by utilizing the current estimates generated by each of its neighbors. Neighbor relations are characterized by a simple, undirected graph mathbb{G} whose vertices correspond to agents and whose edges depict neighbor relations. It is shown that for any nonsingular matrix A and any connected graph mathbb{G}, the proposed algorithm causes all agents' estimates to converge exponentially fast to the desired solution A^{-1}b.

Keywords:Distributed control, Linear systems, Cooperative autonomous systems Abstract: The Bode integral expresses a standard performance limitation for (almost) any controller that asymptotically stabilizes a linear time-invariant system. For the control of distributed systems, spatial invariance allows to write one such "Bode time-integral" per spatial frequency. The present paper inverses the roles of spatial and temporal independent variables in this latter viewpoint. By transposing the notions of controller, causality, and asymptotic stability to the spatial variable, we obtain and interpret "Bode space-integrals", one per temporal frequency. The result directly connects to the notion of string stability.

Keywords:Identification, Network analysis and control Abstract: In this paper, based on the node knock-out procedure, for a networked system consisting of identical multi-dimensional subsystems in which the network structure is unknown and the number of input/output nodes is less than that of subsystems, we propose a novel method to identify the strength of the interaction between nodes even if we do not know any information on the other nodes.

Res. Inst. of Intelligent Control and Systems, Harbin In

Keywords:Distributed control, Agents and autonomous systems, Optimal control Abstract: This paper investigates the stabilization and optimization problems for a group of identically linear agents with undirected interaction topology. It is shown that a distributed control law based on local measurements and relative information exchanged from neighboring agents can be designed for each agent to enable the agent states to be stabilized. Furthermore, due to the use of a parametric Lyapunov approach, the designed distributed control law guarantees not only optimization performance at a network level but also a convergence rate for the group of agents. Finally, a simulation example is provided to demonstrate the advantage as well as the effectiveness of the proposed method.

Keywords:Autonomous robots, Intelligent systems, Optimization Abstract: The Bernstein's problem, asking how to cope with the redundant degrees-of-freedom of musculoskeletal systems in motion control, is straightforwardly extended to more general redundancy resolution problems. What element actions should be coordinated to achieve a complex task, or to realize multi-robot cooperative work?

In this article they are unified and formulated as Generalized Bernstein Problem for developmental realization of complex actions, and then the ease criterion toward a smart solution for the problem is proposed.

Keywords:Robotics Abstract: An asymptotically stable cascaded control algorithm is proposed for cooperative manipulation of a common object. This algorithm controls motion and internal forces of the object, as well as the contact forces between the object and environment. The motion of each manipulator is controlled using an inverse dynamics type of controller. Only knowledge of the kinematics of the manipulated object is required, since the interaction forces and moments between the object and manipulators are measured. The internal stresses in the object are controlled based on enforced impedance relationships between the object and each manipulator. The internal forces and moments are computed using the object kinematics. Contact with the environment is controlled with an enforced impedance relationship between the object and the environment. For both internal and external forces, reference trajectories can be specified. Asymptotic stability of each controller is proven using Lyapunov stability theory and LaSalle’s invariance principle. Guidelines are suggested to compute control parameters of the internal impedance parameters. Merits of the control algorithm are demonstrated in simulations.

CNRS/LAAS and Univ. De Toulouse , UPS, INSA, INP, ISAE

Keywords:Robotics, Autonomous systems Abstract: In this paper, we address the problem of the total visual features loss during visual servoing. We present a new method allowing to reconstruct these features even if the image is completely unavailable. The proposed method has been developed for a 6 degree-of-freedom (DOF) calibrated camera and a static landmark of interest which can be characterized by point features. It relies on a predictor/corrector pair coupled with a depth estimation algorithm. Numerous simulation results are provided and show the relevance of the proposed approach.

Keywords:Robotics, Biomedical systems, Cooperative control Abstract: Motion compensation is a prominent application in robotic beating heart surgery, with significant potential benefits for both surgeons and patients. In this paper we investigate an activate assistance control scheme on a simple tracking task, which helps the surgeon guide the robot on a predefined reference. The control is implemented on top of a shared control system, which serves as a basis for implementing higher level controllers. Experiments with a trained surgeon are also presented, which show the positive effect of the approach.

Keywords:Robotics, Constrained control, Optimal control Abstract: We present a control strategy for a robot that juggles a ball with a single actuated paddle that is attached to the tip of a pendulum-like mechanism. The robot juggles the ball from side-to-side by striking the ball with the paddle when the pendulum reaches its peak angles. Sustained juggling is only possible if the pendulum motion is synchronized to the ball motion. We propose adapting the paddle motion to achieve synchronization. Specifically, we exploit the dynamic coupling between the pendulum and the paddle, which is essentially a moving mass at the tip of the pendulum. Optimal control is used to compute paddle motions that synchronize the pendulum to the ball. Feedback is introduced with a lookup table that maps a measured state to an appropriate paddle motion. In experiments, the proposed feedback strategy enables the robot to juggle at various amplitudes.

Keywords:Linear systems, Uncertain systems, Stability of linear systems Abstract: We address optimal eigenvalue assignment in order to obtain minimum ultimate bounds on every component of the state of a linear time-invariant (LTI) discrete-time system in the presence of non-vanishing disturbances with known constant bounds. As opposed to some continuous-time cases where ultimate bounds can be made arbitrarily small by applying feedback with sufficiently high gain so that the closed-loop eigenvalues are sufficiently fast, the ultimate bound of a discrete-time system with an additive bounded disturbance can never be made smaller than some set that depends on the disturbance bound, even if all closed-loop eigenvalues are set at zero (the fastest possible in discrete-time). In this context, our contribution is twofold: (a) we single out cases where feedback that may not assign all closed-loop eigenvalues at zero achieves the minimum possible ultimate bound for some component of the system state, and (b) by employing an existing componentwise ultimate bound computation formula, we find a class of systems for which assigning all closed-loop eigenvalues at zero indeed yields minimum ultimate bounds. An intermediate result---and our third contribution---in the derivation of (b) is the obtention of the Jordan decomposition that minimises the componentwise ultimate bound formula employed.

Keywords:Lyapunov methods, Uncertain systems, Robust control Abstract: The constrained stabilization of Linear Differential Inclusions (LDIs) via non-homogeneous control Lyapunov functions (CLFs) is addressed in this paper. We consider the class of ``merging'' CLFs, which are composite functions whose gradient is a positive combination of the gradients of two given parents CLFs. In particular, we consider the constructive merging procedure based on recently-introduced composition via R-functions, which represents a parametrized trade-off between the two given CLFs. We show that this novel class of non-homogeneous Lyapunov functions is ``universal'' for the stabilization of LDIs, besides some equivalence results between the control-sharing property under constraints, i.e. the existence of a single control law which makes simultaneously negative the Lyapunov derivatives of the two given CLFs, and the existence of merging CLFs. We also provide an explicit stabilizing control law based on the proposed merging CLF. The theoretical results are finally applied to a perturbed constrained double integrator system.

Keywords:Robust control, Linear time-varying systems, Uncertain systems Abstract: Recent robust stability analysis results for linear time-varying feedback interconnections are based on a time-varying generalisation of the nu-gap metric. The causality of closed-loop mappings is dealt with explicitly, rather than via well-posedness assumptions as is common in the literature. Here, an alternative time-varying gap metric is defined. It is shown that this gives rise to correspondong robust stability results. It is also established that the time-varying gap metric induces the same topology as the generalised nu-gap metric, this being the coarsest under which closed-loop stability and performance are both robust properties.

Keywords:Robust control, Uncertain systems, Flexible structures Abstract: Active vibration control for flexible high-speed rotors tends to be a particularly challenging problem due to the influence of gyroscopic terms, resulting in the need for speeddependent system models. This paper addresses robust control of such systems, using Linear Fractional Transformations (LFTs) for decoupling the system model into speed-dependent and - independent components in LFT feedback. Based on the resulting LFT decomposition, the speed-dependent terms are efficiently reduced in order and considered uncertain with respect to the rotational speed of the shaft. The resulting perturbations are augmented by complex, additive uncertainties and explicitly used for control synthesis. Defining semi-modal performance measures, the perturbed openloop systems are well-suited for mixed µ synthesis techniques. In particular, (D,G)-K and µ-K algorithm, both enabling explicit treatment of mixed perturbations, are investigated in approaching the robust vibration attenuation problem across the range of operating speeds.

Keywords:Robust control, Uncertain systems, Linear parameter-varying systems Abstract: This paper revisits the issue of robust stability analysis of linear interval parameter matrices, which used to be a highly active research topic in the eighties and nineties.The reason for this revived interest in this topic is that the recent research by the authors on Qualitative Stability, a topic of interest in the field of population/community dynamics in ecology is shown to shed considerable insight with possible new results in the robust stability of matrix families. Thus in this paper, we expand on the two notions of robustness introduced recently by the authors, namely `Qualitative Robustness' and `Quantitative Robustness' and investigate their interdependence. Specifically, it is shown that for a class of matrix families with specified `Qualitative Robustness' indices, it is sufficient to check the stability of only `vertex' matrices (i.e. an extreme point solution) to guarantee the robust stability of the entire interval matrix family. This is indeed deemed important and significant because with this result, we can easily identify for which `interval matrix families' we need to resort to more sophisticated stability check algorithms, and for which families we can get away with a ` vertex matrix check' (i.e. an `extreme point solution'). It turns out that this class of `qualitative stable' matrices that admit `vertex solution' for its `quantitative robustness' is quite large. Thus the results of this paper offer new insight into the nature of interactions and interconnections in a matrix family on its robust stability. Encouraged by the results of this paper, continued research is underway in using this interdependence of `qualitative robstness' and `quantitative robustness' in the design of robust controllers for engineering systems.

Keywords:Uncertain systems, Robust control, Randomized algorithms Abstract: The structured singular value mu has been widely studied for uncertain dynamical systems. Recently a great attention is paid to the probabilistic mu problem. Instead of computing the conservative worst-case mu we are interested in the probabilistic distribution of mu, given a probability distribution on the set of uncertainties. Traditionally this problem is solved by Monte Carlo algorithms. In this paper we propose analytic methods to compute the probabilistic mu for rank-one and perturbed rank-one matrices. We expect that these results will provide an algorithm that is not as computationally expensive as the linear cut algorithm in cite{prob_lincut}.

Keywords:Control over communication Abstract: Recently, a finite horizon minimum variance control problem was proposed using feedback over a Gaussian communication channel. Because only the terminal state is penalized, it was shown that linear communication and control strategies are optimal and achieve the information theoretic minimum cost. However, because the transient state is not penalized, the transient behavior can be poor. In the present paper, we show that if there is at most one open loop unstable plant pole, then the transient response will remain bounded as the control horizon tends to infinity, and will approach a value determined by the solution to a certain algebraic Riccati equation.

Keywords:Control over communication, Control over networks, Uncertain systems Abstract: This research addresses stabilization of uncertain systems over data rate constrained and lossy channels. While many of the existing works assume that the packet loss process is independent and identically distributed, we model it as a two-state Markov chain, which can deal with more practical situations including bursty dropouts. For parametrically uncertain plants, a necessary condition and a sufficient condition for mean square stability are derived. These conditions are represented by the product of the eigenvalues of the nominal plants, the data rate, the transition probabilities of the channel states, and the upper bounds of uncertainties. In particular, for scalar plants, the conditions coincide with each other.

Keywords:Control over communication, Network analysis and control, Optimal control Abstract: In this paper we consider the problem of controlling unstable stochastic linear systems in the presence of a communication channel between the sensors and the actuators. We propose an LQG architecture that separates the problem of designing suitable regulators for controlling the plant, referred to as Plant encoder/decoders, from the problem of designing encoder/decoder for the communication channel. We provide a mathematical model that takes into account the most important features of today's wireless communication protocols such as quantization errors, limited channel capacity, decoding delay and packet loss, while still being amenable to analytic treatment. We then restrict our discussion to a special class of linear plant encoder/decoders and to a channel with signal-to-noise (SNR) limitations and packet loss only, and we derive stability conditions and optimal parameters for the controller design in the cheap-control setting. Through this analysis we are able to recover several results available in the literature that treated packet loss and quantization error separately.

Keywords:Optimal control, Control over networks, Control over communication Abstract: This paper is concerned with the optimal LQG control of a system through lossy data networks. In particular we will focus on the case where control commands are issued to the system over a communication network where packets may be randomly dropped according to a two-state Markov chain. Under these assumptions, the optimal finite-horizon LQG problem is solved by means of dynamic programming arguments. The infinite horizon LQG control problem is explored and conditions to ensure its convergence are investigated. Finally it is shown how the results presented in this paper can be employed in the case that also the observation packet may be dropped. A numerical simulation shows the relationship between the convergence of the LQG cost and the value of the parameters of the Markov chain.

Keywords:Control over networks, Stochastic control, Stability of linear systems Abstract: The problem of feedback stabilization of LTI plants over a Gaussian interference channel is considered. Two plants with arbitrary distributed initial states are monitored by two separate sensors which communicate their measurements to two separate controllers over a Gaussian interference channel under average transmit power constraints. The necessary conditions for the mean square-stabilization over a memoryless symmetric Gaussian interference channel are derived. These conditions are shown to be tight for some system parameters. Further it is shown that linear and memory-less sensing and control schemes are optimal for stabilization in some special cases.

Keywords:Control over communication, Optimal control, Stochastic control Abstract: In this paper, the indefinite linear quadratic (LQ) optimal control of continuous-time linear time-invariant systems with random input gains is studied. One main novelty of this work is the use of channel/controller co-design framework which bridges and integrates the design of the channels and controller. The co-design is carried out by the twist of channel resource allocation, i.e., the channel capacities can be allocated among the input channels by the control designer subject to an overall capacity constraint. With the channel/controller co-design, necessary and sufficient conditions for the well-posedness as well as the attainability of the indefinite LQ problem concerned are obtained. The optimal control law is given by a linear state feedback associated with the mean-square stabilizing solution of a modified algebraic Riccati equation.

Keywords:Identification, Signal processing Abstract: In this paper we propose a Maximum a Posteriori (MAP) approach for estimating a random sparse parameter vector in the presence of nonlinearities of unknown parameters. In this Bayesian approach, the a priori probability distribution for the parameter vector is utilised as a mechanism to promote sparsity. We solve this identification problem by using a generalized Expectation Maximization algorithm in a MAP framework.

Keywords:Identification, Signal processing, Fault detection and identification Abstract: In this paper, the properties of two recently proposed frequency-domain subspace-based algorithms to estimate discrete-time cross-power spectral density (cross-PSD) and auto-power spectral density (auto-PSD) matrices of vector auto-regressive moving-average and moving-average (ARMAMA) models from sampled values of the Welch cross-PSD and auto-PSD estimators on uniform grids of frequencies, are illustrated by numerical and real-life application examples. The latter is concerned with the modeling of acoustic spectra for detecting faults in induction motors.

Keywords:Identification, Statistical learning Abstract: In this paper, a general sparse estimator is proposed, based on the maximum likelihood / prediction error method (or any root-N-consistent estimator). This procedure does not rely on the convexity of the cost function of the underlying estimator (in case such estimator is an M-estimator), and it provides an automatic tuning of the (implicit) regularization parameter. The idea behind the proposed method is a three step procedure, where the first step consists in a standard root-N-consistent estimation, the second step seeks for the sparsest estimate in a neighborhood of the initial estimate, and the last step is a refinement based on the sparseness pattern estimated in the second step. A rigorous statistical analysis is provided, which establishes conditions for consistency, asymptotic variable selection and the so-called Oracle property. A simulation example is given to demonstrate the performance of the method.

Keywords:Identification, Stochastic systems, Linear parameter-varying systems Abstract: We study the problem of identifying a finite dimensional linear stochastic SISO system driven by a Levy process. The latter are widely used in modelling financial time series. In a number of important examples the density function of the innovation term is unknown, but its characteristic function is explicitly known, possibly up to a few unknown parameters. In this paper we present and analyze a novel identification method that exploits the information on the characteristic function of the noise. It is obtained by adapting adapting the empirical characteristic function method (ECF for short) developed for i.i.d. samples. We will show that the new method may be more efficient in estimating the system parameters than a plain prediction error method.

Keywords:Identification, Stochastic systems, Modeling Abstract: In this paper, we study modeling and identification of stochastic systems by Generalized Factor Analysis models. Although this class of models was originally introduced for econometric purposes, we present some possible applications of engineering interest. In particular, we show that there is a natural connection between Generalized Factor Analysis models and multi-agents systems. The common factor component of the model has an interpretation as a flocking component of the system behavior.

Keywords:Signal processing, Identification, Aerospace Abstract: State estimation problem for a linear discrete dynamic system is considered. Some components of the state vector can abruptly change under the influence of rare uncontrolled input pulses in the right-hand side of equations. In this case, l_{1}-norm approximation (least absolute deviations method) gives better results than the standard l_{2}-norm approximation (least squares method). A recursive estimation algorithm for finding l_{1}-norm approximation in case of large amount of measurements is presented. To make numerical procedure more reliable, a nonoptimality level for current iteration is constructed. An example from inertial navigation verifies the effectiveness of proposed approach.

Keywords:Fault detection and identification, Nonlinear system theory, Fluid flow systems Abstract: This paper addresses a fault detection and isolation technique for differential flat systems. For such nonlinear systems, it is possible to find a set of variables, named flat outputs such that states and control inputs can be expressed as functions of flat outputs and their derivatives.

Flat systems properties are used to detect and isolate faults and the nonuniqueness property of the set of flat outputs is used for increase the number of residues and improve the fault isolation, the proposed approach will be applied on a classical three tank system.

Keywords:Fault diagnosis Abstract: Polymer Electrolyte Membrane Fuel Cell (PEMFC) is a promising power source for a wide range of applications. Fault diagnosis, especially online fault diagnosis, is an essential issue to promote the development and widespread use of PEMFC technology. This paper proposes a diagnosis approach for large PEMFC stack. In this approach, flooding fault is concerned; individual cell voltages are chosen as original variables for diagnosis. A dimension reduction method Fisher linear discrimination (FDA) is adopted to extract the features from the cell voltage composed vectors. After that, a classification methodology, Gaussian mixture model (GMM) is applied for fault detection. Flooding experiments were conducted on a 20-cell stack to test the approach. The obtained results showed that data points can be classified to different states of health with a high accuracy. It is also verified that the real-time implementation of the algorithm is feasible.

Keywords:Fault diagnosis, Distributed parameter systems Abstract: This paper deals with the problem of designing a robust fault detection methodology for a class of input-output, uncertain dynamical distributed parameter systems, namely mechanical elastodynamic systems, which are representative of a whole class of problems related to on-line health monitoring of mechanical and civil engineering structures. The proposed approach does not require full state measurements and is robust to measuring, modeling and numerical errors, thanks to a time varying detection threshold. In order to avoid the problems associated with classical discretization techniques for distributed parameter systems, which can lead to numerical errors difficult to bound a priori, and thus higher thresholds, a suitable structure-preserving algebraic approach, called Cell Method, will be employed. This method consists in writing the equations of a distributed parameter system directly in discrete form, avoiding the usual discretization process and leading to a symplectic, that is energy preserving, numerical scheme.

Keywords:Fault diagnosis, Identification, Signal processing Abstract: The problem of detecting causality, from routine operating data, is reviewed from a system identification perspective. It is shown that even simple examples from the literature under Granger causality analysis do not have adequate model fit. As an alternative, this study uses the system identification platform to capture causality from process data. For example, the model inadequacy test is considered an important reason to reject a given causal relationship. The rich framework of system identification techniques and the choice of models to deal with exogenous variables and nonlinearities are shown to be an extremely suitable foundation to detect casual relationships. The utility of the proposed approach is illustrated by several benchmark examples including the analysis of routine operating data in an industrial case study.

Keywords:Petri nets, Fault diagnosis, Discrete event systems Abstract: This paper proposes an online approach for the fault diagnosis for time discrete event systems, which are modeled by time Petri net. The observation is given by a subset of transitions whose occurrence is always observable. Faults correspond to a subset of the transitions whose firing are not observable. According to the most of the literature on discrete event systems, we define three fault states, namely N, F and U, corresponding to normal, fault and uncertain states, respectively. The proposed approach use a Fault Diagnosis Graph (FDG). It is adapted from state class graph by keeping only the necessary information for computation of the fault states and removing the unnecessary states. Some algorithms to compute after each observation only part of the FDG required to update the diagnosis states are given.

Keywords:Fuzzy systems, Observers for nonlinear systems, Fault diagnosis Abstract: This article aims the observer synthesis for a class of nonlinear systems and affected by unknown inputs, represented under the multimodel bilinear formulation. Sufficient conditions to design an unknown input fuzzy bilinear observer are given in Linear Matrix Inequalities (LMIs) terms. The paper studies also the problem of fault detection and isolation. An unknown input fuzzy bilinear fault diagnosis observer design is proposed. Numerical example is given to illustrate the effectiveness of the given results.

Keywords:Energy systems, Modeling, Behavioural systems Abstract: Since several years, multi-agent systems have been used for wide range of application areas and particularly in systems modelling and simulation. Those systems are based on the interaction of several individual components, called agents, which are proactive considering interaction with neighbours and with the surrounding environment. The IRTES-SeT laboratory develops a PEM-Fuel Cell model for detailed layer level simulation based on multi-agent paradigm. Whatever the level of abstraction considered, modelling the electrochemical process requires at least: an electrochemical model, a fluidic model, and a thermal model. These elements are integrated into our simulation model at the microscopic level. The goal of this paper is to present a multi-physical micro-level PEM-Fuel Cell model by using a multi-agent approach.

Lab. Systems and Transport, Univ. of Tech. of Belfort

Keywords:Sliding mode control, Observers for nonlinear systems Abstract: In this paper, we propose a differential flatness-based observer for a PEM fuel cell air-feed system. The proposed observer uses the measurements of supply manifold air pressure and compressor mass flow rate in order to estimate the oxygen partial pressure, nitrogen partial pressure and the compressor speed. An adaptive-gain Second Order Sliding Mode differentiator based on super-twisting algorithm is designed to estimate the time derivatives of the system outputs when the boundary of higher time derivative is unknown. Then, the states are estimated based on these values. The objective is to minimize the number of embedded sensors in order to get a precise and economic solution. The feasibility and effectiveness of the proposed approach is demonstrated through simulation results obtained from a nonlinear fuel cell system.

Keywords:Energy systems, Reduced order modeling Abstract: This paper investigates the nitrogen blanketing front during the dead-ended anode (DEA) operation of a PEM fuel cell. It is found that the dynamic evolution of nitrogen accumulation in the DEA of a PEM fuel cell eventually arrives to a steady-state, which suggests the existence of equilibrium. We use a multi-component model of the two-phase, one-dimensional (along-channel) system to analyze this phenomenon. Specifically, the model is first verified with experimental observations, and then utilized to show the evolution toward equilibrium. The full order model is reduced to a second-order partial differential equation (PDE) with one state, which can be used to predict and analyze the observed steady state DEA behavior. The parametric study is performed focusing on the influence of the cathode pressure on the existence of equilibrium in the DEA condition.

Keywords:Energy systems, Sliding mode control, Uncertain systems Abstract: The utilization of solid oxide fuel cells (SOFCs) as well as other high-temperature fuel cells for a decentralized power supply demands for reliable and guaranteed stabilizing control strategies, that are capable of providing electrical and thermal energy. Moreover, it is essential to increase the number of possible thermal cycles of SOFCs by means of control laws which reduce temperature gradients in the space coordinates of a stack module during transient operating conditions. For this purpose, suitable control-oriented system models have been identified in previous work and parameterized reliably by means of both local and global optimization procedures. By exploiting these models, which can be extended to account for parameters that are subject to bounded uncertainty, interval-based sliding mode controllers can be derived. These controllers simultaneously adjust the mass flow and temperature of air supplied to the cathode of the SOFC. In this paper, a real-time capable implementation of the corresponding interval-based sliding mode controller and selected experimental results are presented for an SOFC test rig available at the Chair of Mechatronics at the University of Rostock.

Faculty of Electrical and Computer Engineering, Babol Industrial

Keywords:Energy systems, Sliding mode control Abstract: This paper deals with an high-order sliding-mode approach to the observer-based output feedback control of a PEM fuel cell system comprising a compressor, a supply manifold, the fuel-cell stack and the return manifold. The suggested scheme assumes the availability for measurements of readily accessible quantities such as the compressor angular velocity, the load current, and the supply and return manifold pressures. The control task is formulated in term of regulating the oxygen excess ratio (which is estimated by the observer) to a suitable set-point value by using, as adjustable input variable, the compressor supply voltage. The treatment is based on a nonlinear modeling of the PEM fuel cell system under study. Simulations results showing the feasibility and satisfactory performance of the proposed approach are provided

Keywords:Energy systems, Sliding mode control, Optimization algorithms Abstract: This work presents initial experimental results of an adaptive sliding-mode extremum seeker that minimizes the hydrogen consumption in a fuel cell based system. The extremum seeker is based on the classical steepest-descent method, the main challenge being the fact that the gradient of the objective function is unknown. The gradient is estimated by means of a sliding-mode adaptive estimator. The strategy is applied in experimental practical situations in a fuel cell test bench, this allows to asses the performance of the scheme as well as the difficulties that arise in real applications.

Keywords:Electrical power systems, Optimization, Energy systems Abstract: The large-scale integration of renewable resources has recently raised interest in systematic methods for committing locational reserves in order to secure the system against contingencies and the unpredictable and highly variable fluctuation of renewable energy supply, while accounting for power flow constraints imposed by the transmission network. In this paper we compare two approaches for committing locational reserves: stochastic unit commitment and a hybrid approach of scenario-based security-constrained commitment. Parallel algorithms are developed for solving the resulting models, based on Lagrangian relaxation and Benders decomposition. The proposed algorithms are implemented in a high performance computing environment and the performance of the resulting policies is tested against a reduced model of the California ISO interconnected with the Western Electricity Coordinating Council.

Keywords:Randomized algorithms, Electrical power systems, Robust control Abstract: The increased penetration of renewable energy sources to the network highlights the necessity of constructing stochastic variants of the standard unit commitment and reserve scheduling problems. Earlier approaches to such problems are either restricted to ad-hoc methodologies (at the expense of a suboptimal solution), or lead to computationally intractable formulations. In this paper we provide a unified framework to deal with such planning problems for systems with uncertain generation, while providing a-priori probabilistic certificates for the robustness properties of the resulting solution. Our methodology is based on a mixture of randomized and robust optimization and leads to a tractable problem formulation. To illustrate the performance of the proposed methodology we apply it to the IEEE 30-bus network, and compare it by means of Monte Carlo simulations against an algorithm based on a deterministic variant of the unit commitment problem.

Keywords:Electrical power systems, Optimal control, Linear time-varying systems Abstract: We investigate the potential for aggregations of residential thermostatically controlled loads (TCLs), such as air conditioners, to arbitrage intraday wholesale electricity market prices via non-disruptive direct load control. Since wholesale electricity prices reflect power system conditions, arbitrage provides a service to the grid, helping to balance real-time supply and demand. While previous work on the energy arbitrage problem has used simple energy storage models, we use high fidelity TCL-specific models which allow us to understand and quantify the full capabilities and constraints of these time-varying systems. We explore two optimization/control frameworks for solving the arbitrage problem, both based on receding horizon linear programming. Since we find that the first approach requires significant computation, we develop a second approach involving decomposition of the optimal control problem into separate optimization and control problems. Simulation results show that TCLs could save on the order of 10% of wholesale energy costs via arbitrage, with savings decreasing with price forecast error.

Keywords:Electrical power systems, Energy systems, Optimal control Abstract: This paper proposes a Model Predictive Control (MPC) scheme to control residential buildings with space heating/cooling loads, an Electric Water Heater (EWH), photovoltaics (PV) and battery storage in a time-varying electricity price environment. The controller uses models for the system components as well as predictions for future disturbances such as weather conditions, occupancy and electricity prices to find the building operation that minimizes electricity costs over the prediction horizon while respecting user comfort constraints. The building operation is investigated under three different price scenarios: (1) a simple day-night tariff for end-customers, (2) a day-ahead dynamic tariff reflecting the wholesale market marginal costs and (3) a real-time dynamic tariff. Residential buildings response to such price signals is investigated in a case study and their potential for Demand Response (DR) programs is evaluated.

Keywords:Electrical power systems Abstract: The paper develops a state-space model for the aggregate power drawn by a group of plug-in electric vehicle (PEV) chargers under hysteresis-based charging. The aggregate response of the PEV charging loads to changes in the hysteresis deadband is nonlinear, requiring detailed analysis to accurately capture the dynamics. Related work, which focused on thermostatically controlled loads (TCLs), addressed state-space modelling by dividing the hysteresis deadband into equally sized bins and keeping track of the inter-bin migration of loads. A system of PEV chargers can be treated similarly. A new modelling paradigm has been developed to allow for fast variation of the hysteresis deadband. This model tracks the distribution of PEV chargers within the hysteresis deadband, with the inter-bin migration of chargers used to capture the aggregate dynamics.

Keywords:Electrical power systems, Power plants, Optimization algorithms Abstract: We consider an aggregator managing a portfolio of runtime and downtime constrained ON/OFF demand-side devices. The devices are able to shift consumption in time within certain energy limitations. We show how the aggregator can manage the portfolio of devices to collectively provide upward and downward regulation. Two control strategies are presented enabling the portfolio to provide regulating power while respecting the runtime, downtime, and energy constraints of the devices. The first strategy is a predictive controller requiring complete device information; this controller is able to utilize the full flexibility of the portfolio but can only handle a small number of devices. The second strategy is an agile controller requiring less device information; this controller is able to handle a large number of devices but not able to utilize the full flexibility of the portfolio.

Keywords:Control education, Mechatronics, Predictive control for nonlinear systems Abstract: This paper presents an educational framework based on the Lego Mindstorms NXT robotic platform used to outline both the theoretical and practical aspects of the Model Predictive Control theory. The case of a two-wheeled inverted pendulum is considered as at-size scenario. For such a system, starting from its mathematical modeling, an established design methodology is presented aiming to outline step-by-step the predictive controller implementation on a low-power architecture. The effectiveness of this multidisciplinary approach is illustrated along this presentation and demonstrated with experimental results.

Keywords:Energy systems, Process control, Predictive control for nonlinear systems Abstract: The current work addresses the control issues that arise during the operation of a fuel cell system based on a novel combination of two Model Predictive Control (MPC) strategies, explicit and Nonlinear MPC (NMPC). The proposed framework relies on an NMPC formulation that uses a simultaneous direct transcription dynamic optimization method that recasts the multivariable control problem into a nonlinear programming problem (NLP) using a warm-start initialization method. The performance of the optimizer is improved by a search space reduction (SSR) technique which is based on a piecewise affine approximation (PWA) of the variable’s feasible space, derived offline by a multi-parametric Quadratic Programming (mpQP) method. The behavior of the explicit NMPC (exNMPC) framework is initially explored by a simulation study and subsequently it is experimentally verified through the online deployment to the fuel cell unit, demonstrating excellent response in terms of computational effort and accuracy with respect to the control objectives.

Keywords:Predictive control for linear systems, Decentralized control, Constrained control Abstract: In this paper centralised Model Predictive Control (MPC), tuned in two different ways, and a decentralised control scheme are proposed for the control of the Broken River in Victoria, Australia. The control objective is to improve water resource management for the benefit of irrigators and the environment. The controllers are designed based on simple time delay and integrator delay models. The controllers are evaluated in realistic simulation scenarios and compared to manual operation. The use of control offers increased operational flexibility with a significant potential for substantial water savings, improved level of service to irrigators and improved environmental benefits.

Keywords:Predictive control for linear systems, Energy systems, Large-scale systems Abstract: The method described in this paper balances power production and consumption with a large number of thermal loads. Linear controllers are used for the loads to track a temperature set point, while Model Predictive Control (MPC) and model estimation of the load behavior are used for coordination. The total power consumption of all loads is controlled indirectly through a real-time price. The MPC incorporates forecasts of the power production and disturbances that influence the loads, e.g. time-varying weather forecasts, in order to react ahead of time. A simulation scenario demonstrates that the method allows for the integration of flexible thermal loads in a smart energy system in which consumption follows the changing production.

Keywords:Predictive control for nonlinear systems, Modeling, Differential algebraic systems Abstract: Production of biofuel has a positive environmental and economic impact; therefore, the interest for accurate modeling and more advanced control techniques has grown considerably over the last years. The reason is that it allows optimizing the productivity while the energy consumption is minimized. This paper presents the modeling, simulation and nonlinear control of a double-effect evaporation process to obtain bioethanol from sugarcane juice. This is achieved by controlling the juice concentration at the output of the last evaporator stage. Nonlinear Model Predictive Control (NMPC) has been successfully implemented, following the Extended Prediction Self-Adaptive Control (EPSAC) approach. This algorithm has been chosen among the different methods as it requires less computational load. The effectiveness of the proposed EPSAC controller is presented and compared against PI and Generalized Predictive Control (GPC), through simulation.

Keywords:Safety critical systems, Predictive control for linear systems, Maritime Abstract: In this paper, a governor for marine diesel-electric power plants with a normal and an emergency mode is proposed. In normal mode, variations in the electric frequency are weighed against wear-and-tear of the generator due to thermic variations in the engine. In emergency mode, the governor briefly disregards the wear-and-tear concerns, and attempts to maintain the frequency as steady as possible. This leads to reduced risk of blackout due to larger margins to the underfrequency condition and more reliable connection of additional generating sets to the electric grid. The emergency mode is entered under abnormal conditions only, the overall wear-and-tear resulting from this addition is negligible. The governor is implemented as a moving horizon controller.

Keywords:Sampled data control, Stability of nonlinear systems, Robust control Abstract: This paper is dedicated to the stability analysis of nonlinear sampled-data systems, which are affine in the input. Assuming that a stabilizing continuous-time controller exists and it is implemented digitally, we intend to provide sufficient asymptotic/exponential stability conditions for the sampled-data system. This allows to find an estimate of the upper bound on the asynchronous sampling periods. The stability analysis problem is formulated both globally and locally. The main idea of the paper is to address the stability problem in the framework of dissipativity theory. Furthermore, the result is particularized for the class of polynomial input-affine sampled-data systems, where stability may be tested numerically using sum of squares decomposition and semidefinite programming.

Keywords:Nonlinear system theory, Delay systems, Automotive Abstract: The paper illustrates through the example of a mobile robot, how discretization makes easier the design of a predictor based stabilizer for nonlinear dynamics with delayed input, admitting finite sampled equivalent models.

Keywords:Sampled data control, Stability of linear systems, Linear systems Abstract: Characterisations of "mixed" systems are presented in a discrete-time setting. First, a feedback stability result based on the Nyquist stability theorem is presented. Second, an eigenvalue-based characterisation of "mixed" systems based on their state-space data is derived. The results are analogous to previous results presented for the continuous-time case and provide a foundation for further study concerning the discretisation of "mixed" systems.

Keywords:Sampled data control, Stability of linear systems, Robust control Abstract: This work aims at decreasing the number of sampling instants in state feedback control for perturbed linear time invariant systems. The approach is based on linear matrix inequalities obtained thanks to Lyapunov-Razumikhin stability conditions and convexification arguments that guarantee the exponential stability for a chosen decay-rate. First, the method enables to perform a robust stability analysis regarding time-varying sampling and to maximize a lower-bound estimate of the maximal allowable sampling interval, by computing the adequate Lyapunov-Razumikhin function. Then, it makes it possible to design a state-dependent sampling control scheme that enlarges even further the maximal allowable sampling intervals.

Keywords:Stochastic systems, Delay systems, Discrete event systems Abstract: This paper investigates the stability of linear systems with stochastic delay in discrete time. Stability of the mean and second moment of the non-deterministic system is determined by a set of deterministic discrete-time equations with distributed delay. A theorem is provided that guarantees convergence of the state with convergence of the second moment, assuming that delays are identically independently distributed. The theorem is applied to a scalar equation where the stability of the equilibrium is determined.

Keywords:Computational methods, Identification, Sampled data control Abstract: A new method for numerical simulation and parameter identification of fractional order models is presented in this paper. A Digital Adjustable Fractional Integrator is proposed to improve the numerical simulation of fractional order systems. The main feature of this tool consists in: the important reduction of simulation run time, operate as a one-step forward predictor and, consequently, it can be used for real-time numerical simulation and identification of different fractional order systems using the same structure. The consistence, convergence and stability of the proposed method are proved. Finally, some numerical results are presented to demonstrate that the proposed approximation is a computationally efficient method.

Keywords:Distributed estimation over sensor nets, Observers for linear systems Abstract: We transfer the ideas behind sensitivity-driven distributed model predictive control (c.f. Scheu and Marquardt, 2011) to the moving horizon state estimation problem and present a novel decentralized state estimation algorithm, namely, sensitivity-driven partition-based moving horizon estimation (S-PMHE). We discuss convergence and optimality of S-PMHE for the case of given positive-definite arrival cost weights. Finally, we demonstrate the method on a numerical example.

Keywords:Robust control, Observers for linear systems, Linear parameter-varying systems Abstract: This paper deals with the control of processes having recycle streams. These processes can be modeled as state delayed systems. In this work the problem of robust design of an observed-based controller for these systems is presented. The system is assumed to have norm-bounded uncertainties which are independent in every matrix involved in its state space realization. To ensure asymptotic stability of the closed loop system, a Lyapunov functional is used to obtain delay-independent design conditions. The controller design is accomplished by means of a convex optimization procedure formulated using linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the main characteristics of the proposed design method.

Keywords:Large-scale systems, Observers for linear systems, Linear systems Abstract: In this paper we propose a novel partition-based state estimator for linear discrete-time systems composed of physically coupled subsystems affected by bounded disturbances. The proposed scheme is distributed in the sense that each local state estimator exploits suitable pieces of information from parent subsystems. Moreover, differently from schemes based on moving horizon estimation, it does not require the on-line solution to optimization problems. Our method also guarantees the satisfaction of constraints on local estimation errors. We achieve our aims exploiting the notion of practical robust positive invariance developed in Rakovic et al., 2011. As an example, we illustrate the use of the distributed state estimator for reconstructing the states of a power network system.

Keywords:Filtering, Sensor and signal fusion Abstract: This paper presents a state estimation algorithm referred to as a cubature H_infty information filter (CH_inftyIF) for nonlinear systems. The proposed algorithm is developed from a cubature Kalman filter, an H_infty filter and an extended information filter. The CH_inftyIF is a derivative free filter, where the information state vector and information matrix are propagated rather than the state vector and error covariance matrix. Furthermore, the CH_inftyIF is extended for multi-sensor state estimation. The efficacy of the CH_inftyIF is demonstrated by a simulation example of a permanent magnet synchronous motor in the presence of Gaussian and non-Gaussian noises.

Keywords:Signal processing, Observers for nonlinear systems, Adaptive systems Abstract: The paper deals with an adaptive observer methodology for estimating the parameters of an unknown sinusoidal signal from a measurement perturbed by structured and unstructured uncertainties. The proposed technique makes it possible to handle measurement signals affected by structured uncertainties like, for example, bias and drifts which are typically present in applications. The stability of the estimator with respect to bounded additive disturbances is addressed by Input-to-State Stability arguments. The effectiveness of the proposed technique is shown through numerical simulations where comparisons with some recently proposed algorithms are also provided.

Keywords:Linear time-varying systems, Observers for linear systems, Observers for nonlinear systems Abstract: The problem of interval state observer design is addressed for time-invariant discrete-time systems. Two solutions are proposed: the first one is based on a similarity transformation synthesis, which connects a constant matrix with its nonnegative representation ensuring the observation error positivity. The second contribution shows that in the discrete-time case the estimation error dynamics always can be represented in a cooperative form without a transformation of coordinates. The corresponding observer gain can be found as a solution of the formulated LMIs. The performances of the proposed observers are demonstrated through computer simulations.

Keywords:Optimization, Optimization algorithms, Emerging control theory Abstract: It is well-known that solutions to parametric linear or quadratic programs are continuous piecewise affine functions of the parameter. In this paper we prove the converse, i.e. that every continuous piecewise affine function can be identified with the solution to a parametric linear program. In particular, we provide a constructive proof that every piecewise affine function can be expressed as the linear mapping of the solution to a parametric linear program with at most twice as many variables as the dimension of the image of the piecewise affine function. Our method is illustrated via two small numerical examples.

Keywords:Optimal control, Hybrid systems Abstract: A method for computation of lower and upper bounds for the linear quadratic cost function associated to a class of hybrid linear systems is proposed. The optimization problem involves state space constraints and switches between the continuous and discrete dynamics at fixed time instances on the boundaries of the flow and jump sets. Our approach computes a quadratic suboptimal cost parameterized by initial and end state variables of all time intervals. Then, the unknown parameters are determined via solving constrained quadratic programming problems.

Keywords:Optimization, Process control, Hybrid systems Abstract: A proactive energy management strategy for a stand-alone hybrid renewable energy system is presented. The study was motivated by the system built in Lambton College (Sarnia, Ontario, Canada) which includes photovoltaic arrays, wind turbine, battery, electrolyzers, hydrogen storage tanks, and fuel cells. The control architecture consists of two levels of hierarchy: (1) an optimal predictive scheduling at the supervisory level; (2) system unit control at the low level. A "day-ahead" approach is followed at the supervisory level and a bidirectional communication between the supervisory, proactive control, and the low level control layer. The proposed energy management strategy accounts for external (i.e. weather and demand) and internal disturbances.

Keywords:Energy systems, Hybrid systems Abstract: This paper describes the application of Hybrid Model Predictive Control (HMPC) to a building heating system. The hybrid model contains continuous variables corresponding to physical quantities as well as discrete variables serving as indices of a Linear Time Invariant (LTI) model in action. Two LTI models are considered, each describing different configurations of the building heating system. The application of HMPC allows efficient handling of disturbances by reconfiguration of the heating system. The proposed HMPC strategy improves comfort and reduces energy demands. An exact solution of HMPC is computationally demanding; therefore, three suboptimal solutions are suggested. These take into account specifics of the building heating system and significantly reduce the computational complexity. All presented strategies are compared by means of a numerical simulations using real weather data and a model of a real building.

Keywords:Hybrid systems, Predictive control for nonlinear systems, Modeling Abstract: The current work is motivated by the need of achieving global solution and better computational efficiency for control of any arbitrary nonlinear hybrid dynamical systems (NHDS). In this work, we present a novel modeling and corresponding model predictive control (MPC) formulation for NHDS. The proposed modeling approach relies on disaggregation of polynomials of binary variables that appear in the multiple partially linearized (MPL) model. In particular, we use auxiliary continuous variables and linear constraints to model these polynomials and represent the MPL model in a linear fashion. Subsequently, disaggregation of the variables based multiple models are used to formulate the MPC law for NHDS. The MPC formulation takes similar form as multiple mixed logical dynamical (MMLD) model based MPC and yields a convex MIQP optimization problem. Moreover, the proposed modeling approach results in a compact model than the corresponding MMLD model as it refrains from adding any extra binary variables. Therefore, offers certain computational advantage when used for the predictive control of NHDS. The efficacy of the proposed solution is demonstrated on a three-tank benchmark hybrid system

Keywords:Identification for hybrid systems, Switched systems, Optimization algorithms Abstract: This paper proposes a low-rank and sparse optimization approach to generalized principal component analysis (GPCA) problems. The GPCA problem has a lot of applications in control, system identification, signal processing, and machine learning, however, is a kind of combinatorial problems and NP hard in general. This paper formulates the GPCA problem as a low-rank and sparse optimization problem, that is, matrix rank and l_0 norm minimization problem, and proposes a new algorithm based on the iterative reweighed least squares (IRLS) algorithm. This paper applies this algorithm to the system identification problem of switched autoregressive exogenous (SARX) systems, where the model order of each submodel is unknown. Numerical examples show that the proposed algorithm can identify the switching sequence, system order and parameters of submodels simultaneously.

Keywords:Concensus control and estimation, Markov processes, Quantum information and control Abstract: The analysis of classical consensus algorithms relies on contraction properties of Markov matrices with respect to the Hilbert semi-norm (infinitesimal version of Hilbert's projective metric) and to the total variation norm. We generalize these properties to the case to operators on cones. This is motivated by the study of ``non-commutative consensus'', i.e., of the dynamics of linear maps leaving invariant cones of positive semi-definite matrices. Such maps appear in quantum information (Kraus maps), and in the study of matrix means. We give a characterization of the contraction rate of an abstract Markov operator on a cone, which extends classical formulae obtained by Doe blin and Dobrushin in the case of Markov matrices. In the special case of Kraus maps, we relate the absence of contraction to the positivity of the ``zero-error capacity'' of a quantum channel. We finally show that a number of decision problems concerning the contraction rate of Kraus maps reduce to finding a rank one matrix in linear spaces satisfying certain conditions and discuss complexity issues.

Keywords:Quantum control, Algebraic/geometric methods Abstract: In coherent feedback control schemes a target quantum system S is put in contact with an auxiliary system A and the coherent control can directly affect only A. The system S is controlled indirectly through the interaction with A. The system S is said to be indirectly controllable if every unitary transformation can be performed on the state of S with this scheme. In this paper we show how indirect controllability of S is equivalent to complete controllability of the combined system S+A, if the dimension of A is greater than 2. In the case where the dimension of A is equal to 2, it is possible to have indirect controllability without having complete controllability of S+A and we give sufficient conditions for this to happen. We conjecture that these conditions are also necessary. The results of the paper extend previous results known in the literature relaxing assumptions on the dimensions and on the initial conditions of the systems involved.

Keywords:Quantum control, Emerging control applications, Stability of nonlinear systems Abstract: This paper applies results on the robust stability of nonlinear quantum systems to a system consisting an optical cavity containing a saturated Kerr medium. The system is characterized by a Hamiltonian operator which contains a non-quadratic term involving a quartic function of the annihilation and creation operators. A saturated version of the Kerr nonlinearity leads to a sector bounded nonlinearity which enables a quantum small gain theorem to be applied to this system in order to analyze its stability. Also, a non-quadratic version of a quantum Popov stability criterion is presented and applied to analyze the stability of this system.

Keywords:Quantum control, Lyapunov methods, Stochastic control Abstract: This work treats the problem of generating any desired goal propagator for a driftless quantum system that evolves on the unitary group U(n). The physical relevance of such control problem is the realization of arbitrary quantum gates in quantum computers. Assuming only the controllability of the system, the paper constructs explicit stochastic control laws that assure global asymptotic convergence of the propagator of the system towards the goal propagator. The purpose of introducing a stochastic behaviour in the controls is to speed up convergence. The control strategy can be rigorously proved based on Lyapunov feedback and stochastic techniques. The controls laws rely on a reference trajectory that crosses the desired goal propagator in a time-periodic fashion and such that its corresponding linearised system generates the Lie algebra u(n). Their existence is ensured by the Return Method of Coron, and standard Fourier series results allows them to be explicitly constructed.

Keywords:Quantum control, Stochastic filtering, Observers for linear systems Abstract: The paper is concerned with a problem of coherent (measurement-free) filtering for physically realizable (PR) linear quantum plants. The state variables of such systems satisfy canonical commutation relations and are governed by linear quantum stochastic differential equations, dynamically equivalent to those of an open quantum harmonic oscillator. The problem is to design another PR quantum system, connected unilaterally to the output of the plant and playing the role of a quantum filter, so as to minimize a mean square discrepancy between the dynamic variables of the plant and the output of the filter. This coherent quantum filtering (CQF) formulation is a simplified feedback-free version of the coherent quantum LQG control problem which remains open despite recent studies. The CQF problem is transformed into a constrained covariance control problem which is treated by using the Frechet differentiation of an appropriate Lagrange function with respect to the matrices of the filter.

Keywords:Quantum information and control Abstract: Physical Realizability addresses the question of whether it is possible to implement a given LTI system as a quantum system. It is in general not true that a given synthesized quantum controller described by a set of stochastic differential equations is equivalent to some physically meaningful quantum system. However, if additional quantum noises are permitted in the implementation it is always possible to implement an arbitrary LTI system as a quantum system. In this paper we give an expression for the exact number of noises required to implement a given LTI system as a quantum system. Furthermore, we focus our attention on proving that this is a minimum, that is, it is not possible to implement the system as a quantum system with a smaller number of additional quantum noises.

Keywords:Constrained control, Nonlinear system theory, Lyapunov methods Abstract: It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature.

Keywords:Constrained control, Predictive control for linear systems Abstract: Reference and command governors are predictive add-on schemes that are applied to closed-loop systems and guarantee constraint enforcement while tracking desired reference inputs. This paper introduces two methods for using these predictive methods in the presence of prioritized constraints. The ﬁrst method handles the case of “soft” constraints by using a slack variable to relax the constraints. The second method prioritizes the reference inputs, enforcing the constraints by modifying the lower priority reference inputs ﬁrst. Two examples are reported consisting of a constrained spring-mass-damper system and an F-16 aircraft with actuator constraints.

Keywords:Constrained control, Optimization, Randomized algorithms Abstract: In this paper, we address finite-horizon control for a stochastic linear system subject to constraints on the control and state variables. A control design methodology is proposed where the appropriate trade-off between the minimization of the control cost (performance) and the satisfaction of the state constraints (safety) can be decided by introducing appropriate chance-constrained problems depending on some parameter to be tuned. From an algorithmic viewpoint, a computationally tractable randomized approach to find approximate solutions which are guaranteed to be feasible for the original chance-constrained problem is proposed. A numerical example concludes the paper.

Keywords:Stochastic systems, LMI's/BMI's/SOS's, Constrained control Abstract: This paper is concerned with the design of linear state feedback control laws for linear systems with additive Gaussian disturbances. The objective is to find the feedback gain that minimizes a quadratic cost function in closed-loop operation, while observing chance constraints on the input and/or the state. It is shown that this problem can be cast as a semi-definite program (SDP), in which the chance constraints appear as linear or bilinear matrix inequalities. Both individual chance constraints (ICCs) and joint chance constraints (JCCs) can be considered. In the case of ICCs only, the resulting SDP is linear and can be solved efficiently as a convex optimization program. In the presence of JCCs the SDP becomes bilinear, however it can still be solved efficiently by an iterative algorithm, at least to a local optimum. The application of the method is demonstrated for several numerical examples, underscoring its flexibility and ease of implementation.

Keywords:Process control, Robust control, Constrained control Abstract: In modern synchrotron machines, electrons travelling at relativistic speeds in a closed circular path are bent by strong electromagnetic fields, which cause the electrons to lose energy in the form of synchrotron radiation. In order to achieve optimum performance, electron beam stability is a crucial parameter for modern synchrotrons. In particular, sub-micron stability is now a common requirement for the vertical position of the beam and to achieve the required performance, beam stabilisation feedback systems are used. A common nonlinearity encountered with the actuators in synchrotron feedback systems are the slew rate limits that are included in the circuits that apply power to the magnets in order to limit voltage changes. The large dimensions of synchrotron feedback systems and fast sample rates mean that robust Model Predictive Control (MPC) is not feasible. Therefore, for this application, anti-windup techniques for rate constrained nonlinearities are appropriate. The approach in this paper is anti-windup synthesis based on Internal Model Control (IMC) where it is demonstrated how IMC anti-windup synthesis for static constraints can be extended to rate constraints to improve constrained performance and guarantee stability. An Integral Quadratic Constraint (IQC) framework is used to analyse the robust stability of the system in the presence of both rate constraints and an infinity norm bounded uncertainty. Robust stability tests results and simulation of the anti-windup performance using machine data of the implementation of the control design on the Storage Ring of the UK's national synchrotron facility, Diamond Light Source are presented.

Keywords:Constrained control, Nonlinear system theory, Algebraic/geometric methods Abstract: We present a method for the exact computation of null-controllable sets for single-input bilinear systems with input and state constraints. The proposed approach is based on first linearizing the bilinear system exactly, and applying known methods for the recursive calculation of null-controllable sets subsequently. While these steps are obvious from a conceptual point of view, it has to be taken into account that the constraints are transformed in the exact linearization step. Unfortunately, the transformed constraints are in general non-convex, even if the original constraints are convex. We show how to represent the transformed constraints in terms of a finite number of convex sets, which is instrumental for the computer-based evaluation of the null-controllable sets.

Keywords:Large-scale systems, Cooperative control, Distributed cooperative control over networks Abstract: In this work, synthesis and closed-loop operation of robust distributed model predictive control (MPC) for linear systems using distributed optimization is discussed. Previous work has shown that a nominal MPC controller for this setup can be synthesized and operated in a purely distributed manner. This paper extends this concept to linear systems subject to additive bounded disturbance. It is shown how well-established robust MPC approaches can be applied to distributed systems. The main focus of the paper is on a thorough discussion of computational issues arising from distributed synthesis and closed-loop operation of existing robust MPC controllers. In particular, techniques for distributed synthesis of structured robust positive invariant sets and distributed constraint tightening are proposed. The paper is concluded by a numerical example which illustrates the functionality and performance of the proposed techniques.

Keywords:Distributed control, Energy systems, Predictive control for linear systems Abstract: This work presents a distributed model predictive control scheme for energy distribution. The energy is supposed to be supplied by a renewable power system whose energy production is limited and demanded by several consumers. Therefore, in some cases the produced energy cannot fulfill the energy requirements of the consumers. The proposed controller allows to distribute equitably the produced energy to these consumers without harming any of them. Moreover, simulated results based on a real case are presented in order to assess the proposed control strategy.

Keywords:Agents and autonomous systems, Supervisory control, Stochastic systems Abstract: We consider the problem of satisfying a set of objectives over a collection of agents. For a single agent, the optimal solution can be obtained via a stochastic reachability framework where optimal control policies come along with a performance metric, defined as the probability of successfully achieving a specified objective. As the number of agents increases, the approach quickly becomes computationally expensive and often intractable. We propose a method which includes an advisory controller that allocates tasks among agents based on their ability of handling individual objectives. This ability is encoded by the stochastic reachability performance metrics. The proposed method is tailored to an autonomous surveillance system composed of pan-tilt-zoom (PTZ) cameras and verified experimentally.

Keywords:Large-scale systems, Optimal control, Predictive control for linear systems Abstract: In this paper we describe an efficient implementation of a discrete-time model predictive controller for coordinated control of large-scale distributed systems. The approach is based on parametrization and splitting of the underlying optimization problem into local optimization problems coupled via one coordination problem. The local problems are solved off-line using the multi-parametric optimization approach. The coordination problem is solved on-line at every time step, on a centralized control hardware. Due to the properties of local parametric solutions the coordination problem has a specific structure that can be utilized to solve the on-line problem very efficiently. In case when there is only one linear coupling constraint between subsystems, the on-line computation time can be drastically decreased. The efficiency of proposed controller implementation is depicted on a design of the optimal wind farm controller applicable for implementation on very large wind farms.

Keywords:Optimization algorithms, Randomized algorithms, Distributed control Abstract: In this paper we develop a random coordinate descent method suitable for solving large-scale sparse nonconvex optimization problems with composite objective function. Under the typical assumptions of nonconvexity of the smooth part of the objective function and separability and convexity of the nonsmooth part (e.g. l_1 regularization, box indicator functions or others), we derive an algorithm with a very simple and cheap iteration. We prove sublinear convergence rate for our method to a stationary point. Numerical results show that our algorithm performs favourably in comparison to other algorithms on large-scale sparse nonconvex problems, e.g. the eigenvalue complementarity problem arising in different areas such as stability of dynamical systems, distributed control and resonance frequency of mechanical structures with friction.

Keywords:Optimization, Distributed cooperative control over networks, Agents and autonomous systems Abstract: The paper deals with the coordination of dynamical systems by distributed model predictive control. We consider a set-up in which the subsystems dynamics are decoupled, while the subsystems outputs are coupled by some constraint. Starting from a well established non-iterative and non-cooperative architecture, we provide a novel interpretation for this noncooperative scheme as a simplicial approximation of a convex program. Thanks to this novel interpretation, we are able to show why the existing algorithm, while guaranteeing feasibility, fails to compute an optimal solution to the centralized problem. Furthermore, by exploiting the simplicial approximation structure, we are able to propose a novel algorithm. The proposed algorithm inherits all the properties of the existing one, namely little communication, and feasibility. Furthermore, increasing the communication among the subsystems between two control updates improves the performance of the algorithm, regaining in the limit optimality in a cooperative sense.

Keywords:Agents and autonomous systems, Cooperative autonomous systems, Autonomous robots Abstract: In this paper two related problems are studied: the control of the algebraic connectivity and clustering of a network of single-integrator agents. A steepest-descent algorithm is presented for the first problem, so that a smooth approximation of the algebraic connectivity of the underlying undirected communication graph converges to an assigned value. For the second problem, a new gradient-based control strategy is proposed to automatically partition the mobile robotic network into two predefined groups: our spectral-clustering method leverages a continuous-time power-iteration algorithm on the normalized Laplacian matrix which provides an estimate of its Fiedler vector at each time instant. The results of numerical simulations are provided to illustrate our theoretical findings.

Keywords:Agents and autonomous systems, Cooperative control, Switched systems Abstract: This paper aims to extend the nonnegative matrix theory, which is widely employed for multiple integrator agents, to deal with the consensus control of generic linear multi-agent systems (MASs) under directed dynamic topology. It is finally shown that the exponential consensus can be reached under very relaxed conditions, i.e., the directed interaction topology is only required to be repeatedly jointly rooted and the exponentially unstable mode of each individual system is weak enough. Moreover, a least convergence rate and a bound for the unstable mode of the individual agent system, both of which are independent of the switching mode, can be explicitly specified.

Keywords:Cooperative autonomous systems, Concensus control and estimation, Agents and autonomous systems Abstract: This paper deals with the design of cooperative control laws for nonlinear multi-agent systems. On the first hand, the control objectives are to ensure that a group of agents reaches a time-varying circular formation characterized by some external references representing the position of the center of the formation and its derivatives. In order to reduce the amount of information to be shared, the second part of the paper considers the situation where only the velocity of the center of the formation is available to each agent. Then a distributed consensus algorithm is provided in order to satisfy the same control objectives. Finally, an application to the source-seeking problem is proposed to emphasize previous contribution. These results are supported through computer simulations.

Keywords:Cooperative autonomous systems, Decentralized control, Communication networks Abstract: This paper is concerned with collision-free vehicle formation control when the inter-vehicle network topology is time-varying. Like typical collision-free formation control approaches, the proposed control approach involves two control phases: one for converging to a desired formation (no collision avoidance considered); the other for achieving collision avoidance. However, the proposed control approach has two distinctive features. First, the proposed control approach uses a fixed set of time-invariant control gains for achieving the desired formation but allows time-varying control gains only for avoiding collision. This feature lends itself well to the increase (and the decrease) of the controller's reliability (and complexity) during the most of manoeuvring periods. Second, the proposed control approach provably works for arbitrarily switching network topologies. Theoretical and numerical evidences are provided to justify these two features.

Keywords:Cooperative control, Agents networks, Distributed cooperative control over networks Abstract: In this paper, presented is an approach for the control of swarm motions that treats a swarm as a deformable body or a continuum. By considering a special class of motion maps between a current configuration prescribed at a given time t and a desired configuration prescribed at a subsequent time t+∆t called a homogeneous map two strategies are proposed for the control of a swarm or a multi-agent system (MAS). In the first strategy, MAS motion control is achieved with no communication among agents in the idealized case where the required map from any t to t+∆t may be pre-determined. It is the case when a desired swarm task can be scripted ahead of time with some certainty. The second control strategy is based on three leaders prescribing the motion map for a desired swarm task which is then propagated to the followers via a local inter-agent communication protocol. The proposed communication protocol exploits some special features of homogeneous maps. It achieves the desired MAS motion control with three leaders and minimum inter-agent communications. Simulation results validate the effectiveness of the proposed strategies.

Keywords:Distributed cooperative control over networks, Concensus control and estimation, Agents networks Abstract: This paper deals with the source-seeking problem in which a group of autonomous vehicles must locate and follow the source of some signal based on measurements of the signal strength at different positions. As recently suggested, the gradient of the signal strength can be approximated by a circular formation of agents via a simple weighted average of the signal measured by the agents. Using this result, we propose a distributed source-seeking algorithm based on a consensus method which is guaranteed to steer the circular formation towards the source location using the estimated gradient direction. The proposed algorithm is provided with two tunable parameters that allow for a tradeoff between speed of convergence, noise filtering and formation stability. The benefit of using consensus-based algorithms resides in a more realist discrete time control of the agents and in asynchronous communication resilient to delays which is particularly relevant for underwater applications. The analytic results are finally complemented with numerical simulations.

Keywords:H2/H-infinity methods, Robust control, Model/Controller reduction Abstract: In this paper, a fixed order H-infinity synthesis is used to directly shape the open loop transfer function so that it matches as closely as possible, in the singular values sense, a desired frequency gain which captures both performance and robust stability objectives. First, a loop shaping weight is automatically computed, and then it is used in the controller synthesis by solving a well-suited four-block H-infinity control problem with a recently developed nonsmooth H-infinity synthesis routine. Two industrial applications are provided to illustrate the potential of the approach for low order robust controller design: a first one on the control of a piezo-actuated optronic mechanism, a second one dealing with inertial Line Of Sight stabilization loops.

Keywords:Uncertain systems, Delay systems, H2/H-infinity methods Abstract: An H-infinity control problem for linear systems with point-wise and distributed state delays is considered. The case, where the output equation does not contain the control variable, is treated. In this case, the problem is singular, i.e., the game-theoretic Riccati equation approach is not applicable to its solution. A method of solution of this problem, based on its regularization and asymptotic solution of the regularized problem, is proposed.

Keywords:Robust adaptive control, Observers for nonlinear systems, Adaptive control Abstract: Design of adaptive observers has been an active field in the systems theory. Until know, most of the existing solutions use a class of regular form with a set of unknown parameters. A different scheme used an estimation of external perturbations that can be compensated by the adaptive gain associated to the observer. In this paper, the presence of external perturbations for a model defined by a chain of integrators is considered. The adaptive observer used an identifier to obtain the time varying parameters used by the observer. Simultaneously, an adaptive gain associated to the observer adjusts the observer trajectories to provide the convergence between the states of the uncertain nonlinear system and the ones associated to the estimator suggested in this paper. Once the states of the uncertain system were obtained, a simple feedback controller was able to reject actively the perturbations that affect the nonlinear system. A simple third order uncertain system was evaluated in a numerical simulation for proving the performance of this observer/identifier. The same system was controlled using the estimated trajectories provided by the observer.

Keywords:Servo control, Robust control, LMI's/BMI's/SOS's Abstract: A ball-on-plate balancing system, the ball and plate, has a camera to catch a ball position and a plate whose angle of inclination is limited. This paper proposes a design method of PID control based on the generalized Kalman-Yakubovich-Popov lemma for the ball and plate. The design method has two features: the first one is that a structure of the controller is called I-PD to suppress a large input signal against a major change of the reference signal; the second one is that a filter is introduced into the feedback loop to reduce an influence of the noise measurement from the camera. Both simulation and experiment evaluate the effectiveness of the design method.

Keywords:Robust control, Uncertain systems, Stability of linear systems Abstract: In this paper, we propose a robust controller using a modified disturbance observer (DOB). This modification is asked because the conventional DOB structure does not provide with any means to tune the high-frequency response. Since the measurement noise is significant in the high-frequency range, the performance against the noise in the conventional DOB control system cannot be better than that of the closed-loop system without DOB. Inspired by the new structure given in (Xie, 2010), we propose a modified disturbance observer structure, and present a necessary and sufficient condition for robust stability of the actual closed-loop system. Illustrative examples are included to show the effectiveness of the proposed design.

Keywords:Robust control, Optimal control, Linear systems Abstract: Given a linear plant and a feedback controller it is natural to ask: How much uncertainty can be tolerated by the closed-loop while achieving a specified level of performance? In this paper, a characterization of this question is formulated in terms of a constrained optimization problem; the cost reflects the size of non-constant weights used to quantify system uncertainty across frequency and the constraint is a structured singular value characterization of the required level of robust performance. In the case of unstructured uncertainty the problem can be solved via a family of problems that are convex pointwise in frequency. An iterative algorithm is developed for the case of structured uncertainty.

Keywords:Adaptive control, Mechatronics, Robust adaptive control Abstract: The adaptive regulation is an important issue with a lot of potential for applications in active suspension, active vibration control, disc drives control and active noise control. One of the basic problem from the "control system" point of view is the rejection of multiple unknown and time varying narrow band disturbances without using an additional transducer for getting information upon the disturbances. An adaptive feedback approach has to be considered for this problem. Industry needs a "state of the art" in the field based on a solid experimental verification on a system using a current used technology. The paper present a benchmark problem for suppression of multiple unknown and/or time-varying vibrations and an associated active vibration control system using an inertial actuator on which the experimental verifications will be done. The objective is to minimize the residual force by applying an appropriate control effort through the inertial actuator. The system does not use any additional transducer for getting in real time information upon the disturbances. The benchmark has three levels of difficulties and the associated control performance specifications are presented. The results of the contibutors have been evaluated on a simulator and on the experimental facilities located at GIPSA-LAB, Grenoble, France. An extensive comparison of the results obtained by various approaches is presented.

Keywords:Adaptive systems, Mechatronics Abstract: The problem of adaptive attenuation of a disturbance formed as a finite sum of unknown sinusoidal signals is solved for a discrete-time plant with unstable zeros. It is assumed that a reliable model of the plant is known and the system is internally stable. We propose to construct a control signal as a linear combination of outputs of carefully chosen filters. The coefficients of the combination are tuned via an on-line identification based on the plant model. However, our approach avoids constructing an inverse of the plant model. The technique is applied to a case study on a challenging benchmark example in the field of active vibration control. Attenuation of a disturbance formed as a sum of up to three unknown/time-varying sinusoidal signals is demonstrated via simulation and experimental studies.

Keywords:Adaptive control, Mechatronics, Robust adaptive control Abstract: The paper will compare the performances which can be obtained using a direct adaptive regulation scheme based on the Youla-Kucera (YK) parametrization of the controller and using an adaptive finite impulse response (FIR) filter for implementing the internal model of the disturbance with a new indirect adaptive regulation scheme. The main features of this new scheme are: (i) the use of adaptive Band-stop Filters (BSFs) tuned at the frequencies of the disturbance instead of the Internal Model Principle (IMP) and (ii) a procedure for direct identification of frequencies contained in the disturbance. The use of adaptive BSFs allows to introduce the desired attenuation of the disturbance (instead of total rejection) and allows to get a much better shaping of the output sensitivity function (to meet the specification for the tolerated amplification outside the frequencies of the disturbance). The two approaches are comparatively evaluated on the benchmark simulator and on the benchmark active vibration control system.

Keywords:Adaptive control, Robust adaptive control, Mechatronics Abstract: This paper proposes a methodology to adaptively reduce time varying and narrow band harmonic disturbances via the estimation of a feedback controller transfer function parameterized in a Youla-Kucera parametrization. The proposed adaptive feedback regulation simultaneously minimizes the variance of a performance (output) signal and a control (input) signal in real-time. Uncertainty on the plant dynamics is taken into account by including a frequency weighting on the control signal and the solution is formulated as a Recursive Least Squares minimization. The methodology is applied to a mechanical vibration control benchmark that is part of a collaborative invited session at the conference to demonstrate how the proposed adaptive feedback regulation can effectively reduce unknown harmonic disturbances with time-varying frequency contents.

Keywords:Adaptive control, Servo control Abstract: This paper presents an adaptive control scheme for identifying and rejecting unknown and/or time-varying narrow-band vibrations. We discuss an idea of selective model inversion (SMI) for a (possibly non-minimum phase) plant dynamics at multiple narrow frequency regions, so that vibrations can be estimated and canceled by feedback. By taking advantage of the structure of the disturbance model, we can reduce the adaptation to identify the minimum amount of parameters, achieve accurate parameter estimation under noisy environments, and flexibly reject the narrow-band disturbances with clear tuning intuitions. Evaluation of the proposed algorithm is performed via simulation and experiments on a benchmark system for active vibration control.

Keywords:Mechatronics, Adaptive control, Robust control Abstract: We present in this paper our preliminary results on the problem of learning-based adaptive trajectory tracking control for electromagnetic actuators. First, we develop a nominal nonlinear backstepping controller that stabilizes the tracking errors asymptotically and globally. Second, we robustify the nominal controller using a model-free learning technique, namely, multiparameter extremum seeking, to estimate the uncertain model parameters. In this sense we are proposing to solve an adaptive control problem with model-free learning-based algorithms. We show the performance of the proposed controller on a numerical example.

Keywords:Adaptive systems, Nonlinear system identification, Signal processing Abstract: Model structure selection is a crucial task in applications where nonlinear black-box models are used, in order to reduce the model size and the associated computational effort. One such application is Active Noise Control (ANC), where nonlinear effects arise due e.g. to saturation and distortion of microphones and loudspeakers. Both parameter estimation and model selection are complex in the general nonlinear case if standard algorithms of the Least Mean Squares (LMS) type are used, due to the inherent difficulties in the gradient calculation when the secondary path is nonlinear. A model selection method is here proposed that employs a gradient-free parameter estimation algorithm to tackle the secondary path issue. A virtualization scheme is used to estimate the performance of the model subject to various different structural modifications, in order to select the most appropriate one to apply to the actual control filter. Some simulation examples are discussed to show the effectiveness of the algorithm.

Keywords:Chaotic systems, Nonlinear system identification Abstract: This paper proposes a new matrix method to solve the inverse problem for the Frobenius-Perron equation. The method can be used to construct a piecewise linear Markov transformation, which approximates the evolution of an unknown dynamical system, based on a sequence of observed probability density functions generated by the system. This particular nonlinear system identification problem is solved using a three-step approach which involves determining the Markov partition, the matrix representation of the Frobenius-Perron operator and finally the corresponding point transformation. A numerical example is used to demonstrate the applicability of the approach.

Keywords:Identification, Model validation, Nonlinear system identification Abstract: Set-based estimation for nonlinear systems is a useful tool to handle sparse and uncertain data. The tool provides outer bounds on feasible parameter sets and reachable states, as well as provable inconsistency certificates for entire parameter regions. In case of errors in the data such as outliers or incorrect a priori assumptions on variable uncertainties, set-based approaches can, however, lead to poor estimates or even rejection of a consistent model. We present a set-based approach to systematically identify outliers or incorrect variable uncertainty assumptions. The basic idea is to detect outliers by quantifying the influence they have on the inconsistency of an underlying feasibility problem. The results build on a set-based estimation framework that employs convex relaxations. Specifically we derive model consistency measures and sensitivity measures that combine the sensitivity information stored in the Lagrange dual variables. An algorithm is developed that iteratively detects outliers that contribute most to inconsistency. The algorithm terminates once the data and model are no longer proved inconsistent. The approach is illustrated with an example.

Keywords:Identification, Model/Controller reduction, Autonomous systems Abstract: This paper presents a minimal modelling methodology for capturing highly non-linear dynamics in an electromechanical cart system. The second order differential equation model describing the cart system is reformulated in terms of integrals to enable a fast method for identification of both constant and time varying parameters. The model is identified based on a single experimental proportional step response and is validated on a proportional-derivative (PD) controlled step input for a range of gains. Two models with constant damping and time varying non-linear damping were considered. The fitting accuracy for each model was tested on three separate data sets corresponding to three proportional gains. The three data sets gave similar non-linear damping models and in all cases the non-linear model gave smaller fitting errors than thelinear model. For the PD control responses, the constant damping model gave average percentage prediction errors of 9.3% and the non-linear model gave errors of 3.7%. The non-linear model also provided significantly better PD control design. These results demonstrate the ability of the proposed method to accurately capture significant non-linearities in the data. Computationally, the proposed algorithm is shown to be significantly faster than standard non-linear regression.

Keywords:Nonlinear system identification, Control courses and labs, Control education Abstract: System identification is a fundamentally experimental field of science in that it deals with modeling of system dynamics using measured data. Despite this fact many algorithms and theoretical results are only tested with simulations at the time of publication. One reason for this may be a lack of easily available live data. This paper therefore presents three sets of data, suitable for development, testing and benchmarking of system identification algorithms for nonlinear systems. The data sets are collected from laboratory processes that can be described by block – oriented dynamic models, and by more general nonlinear difference and differential equation models. All data sets are available for free download.

Keywords:Optimization algorithms, Nonlinear system identification, Uncertain systems Abstract: This paper is about optimal experiment design for uncertain nonlinear dynamic processes. We are interested in designing experiments which allow to identify the unknown states and parameters of a differential equation from noisy measurements. Here, unpredictable process noise or structural model-plant mismatches can be an additional complication. In this case, robustness aspects have to be taken into account as the experiment has to be planned under incomplete information. The paper discusses problem formulations and numerical solution approaches for this type of robust optimal experiment design problems under various assumptions on the uncertainties. The corresponding techniques are illustrated in the design of experiments for a fedbatch bioreactor.

Keywords:Agents networks, Fault tolerant systems, Decentralized control Abstract: The paper faces a fault-tolerant control problem for a network of agents with single-integrator internal dynamics, which share information on their states according to an arbitrary topology. Specifically, we aim at designing a decentralized regulator able to place the closed-loop dominant poles near prespecified locations. Furthermore, this goal has to be achieved even in the presence of faults of the transmitting and receiving apparatuses of the single agents. We prove a necessary and sufficient solvability condition for our pole-placement problem, and show that it can be solved if and only if a simpler fault-tolerant stabilization problem admits a solution. Then, we give an explicit formula for a class of possible regulators.

Keywords:Fault tolerant systems, Linear parameter-varying systems, Autonomous robots Abstract: Fault-tolerant control (FTC) allows to preserve performance and stability despite the presence of faults. The literature considers two main groups of techniques: the passive and the active FTC techniques. In case of the passive techniques, the fault is taken into account as a system perturbation, so that the control law has fault capabilities that allow the system to cope with the fault presence. On the other hand, in the case of the active FTC techniques, the control law uses some information given by a Fault Detection and Isolation (FDI) module, so that through some automatic adjustment in the control loop, the fault is tolerated with minimum performance degradation. In this paper, a linear parameter-varying (LPV)/linear matrix inequalities (LMIs)-based technique is used to achieve fault tolerance and to compare benefits and drawbacks of passive and active FTC. The proposed approach is applied to a two-wheel differential robot.

Keywords:Fault tolerant systems, Linear parameter-varying systems, Stability of linear systems Abstract: This paper presents the results of a Fault Tolerant Control based on observers for polynomial LPV systems. The main contribution lies in observers, controller, Fault Diagnosis and Isolation unit and Fault Tolerant Control (FTC) design procedure, based on the solution of Parameterized Linear Matrix Inequalities (PLMI) with application to a riderless bicycle dynamics. Further, unlike previous works, this approach takes for its design only the measured outputs provided by the in-built bicycle prototype sensors, eliminating the necessity of additional computations for the control law. The previous fact is viewed as an additional contribution in this development.

Keywords:Fault tolerant systems, Process control Abstract: The selection of the control structure, which is a specification of the interconnection of measurements, exogenous inputs, and manipulated variables, is a critical step in the design of a control system. This paper presents a general internal model control structure with multiple degrees-of-freedom in which each controller is independently designed. The control system is shown to remain optimal when controllers are taken off-line due to component failures, without requiring re-design of any of the on-line controllers. The optimality of the proposed approach is demonstrated for the control of a simulated thin-film process for a variety of component failures.

Keywords:Modeling, Fault tolerant systems, Automotive Abstract: The aim of this paper is to provide a dynamic model of the Toyota Hybrid System (THS) for simulation and control purposes in the case of fault of one of the electric machines. The two three-phase electric machines that are commonly used in THS are here replaced by two five-phase machines. The model of the whole system is realized by using the Power-Oriented Graphs modeling technique and includes the dynamics of the engine, electric machines, planetary gear, transmission and vehicle. A rule-based control strategy is used to operate the vehicle in different operation modes and a fault-tolerant control is applied in the case of electrical machine failure. Simulation results are given in both healthy and fault condition to show the effectiveness of the dynamic model and the robustness of the proposed control.

Keywords:Fault tolerant systems, Statistical learning, Neural networks Abstract: Efficient heat, ventilating and air-conditioning (HVAC) systems is one of the big challenges today around the world. The fault detection and isolation (FDI) play a significant role in the monitoring, repairing and maintaining of technical systems for the final destination of cost reduction. FDI makes it possible to reduce total cost effective of maintenance and thus increase the capacity utilization rates of equipment. Reduction of energy wasting in the system by on time fault detection is another goal. Therefore, this work proposes a new fault detector based on a black box Neural Network (ANN) model and online support vector machines (SVM) classifier which integrates a dimension reduction scheme to analyze the failure of air fan supply and dampers fault. The key advantage of this algorithm is to make robustness for SVM to recognize a faulty condition with unexpected sensors values. The NN generate a high accurate model which is based reference for SVM classifier. Now by using this black box model we make possibility of robustness for SVM to increase detection probability. Finally, a series of faulty experimental data are applied to evaluate the effectiveness of the robust classifier. Final results show that online SVM can detect accurately the air supply fan fault and damper fault of a HVAC system with minimum usage data. It is also outperforms offline SVM on such energy systems for classification.

Keywords:Filtering, Maritime, Observers for nonlinear systems Abstract: This paper presents a novel navigation filter for estimation of linear motion quantities based on a combined Long Baseline / Ultra Short Baseline (LBL/USBL) acoustic positioning system with application to underwater vehicles. The filtering algorithm does not resort to any algebraic inversion techniques and no linearizations are carried out whatsoever. In this way, the nonlinear sensor-based system dynamics are considered to their full extent and globally asymptotically stable (GAS) error dynamics are achieved. Finally, it is shown, under simulation environment, that the filter achieves very good performance in the presence of sensor noise.

Keywords:Observers for nonlinear systems, Maritime, Robotics Abstract: Typical attitude estimation solutions for underwater vehicles rely on magnetometers, which are prone to magnetic field distortions. This can preclude its use in intervention scenarios, in the vicinity of objects with strong magnetic signatures, severely endangering not only the intervention mission but also the operation of the underwater vehicle. This paper presents a novel attitude estimation solution, based on a combined Long Baseline / Ultra Short Baseline (LBL/USBL) acoustic positioning system, with application to underwater vehicles. The range and range differences of arrival obtained with the LBL/USBL are directly embedded in the estimator dynamics, without any linearization whatsoever, and globally exponentially stable (GES) error dynamics are achieved. Simulation results evidence good performance of the proposed solution.

Keywords:Identification, Model validation, Maritime Abstract: An assessment of a statistical model currently used for the prediction of high tides in the Venetian lagoon is presented. The model is analyzed from several points of view and is compared with state-space descriptions of smaller order which seem to provide slightly better results. Moreover the relevance of additional external inputs to the model, that is additional meteorological agents, is discussed.

Keywords:Maritime, Predictive control for linear systems, Identification for control Abstract: The purpose of this study is to improve a mooring system with Controllable Pitch Propeller (CPP). Because of the slip of propeller, velocity response of CPP has time delay. In this study, the ship’s propelling force with the CPP’s angle was identified on an actual ship and delay time was observed by analyzing the data of propelling force. Then the CPP angle is controlled by using Generalized Minimum Variance Control (GMVC) to obtain better performance for the mooring system.

Keywords:Maritime, Predictive control for nonlinear systems, Autonomous systems Abstract: This paper presents a solution to the problem of trajectory tracking control for autonomous surface craft (ASC) in the presence of ocean currents. The proposed solution is rooted in nonlinear model predictive control (NMPC) techniques and addresses explicitly state and input constraints. Whereas state saturation constraints are added to the underlying optimization cost functional as penalties, input saturation constraints are made intrinsic to the nonlinear model used in the optimization problem, thus reducing the computational burden of the resulting NMPC algorithm. Simulation results, obtained with a nonlinear dynamic model of a prototype ASC, show that the NMPC strategy adopted yields good performance in the presence of constant currents. Experimental results are also provided to validate the real-time implementation of the proposed techniques.

Keywords:Maritime, Reduced order modeling, Identification Abstract: In this paper, the problem of designing a Boat Parking Assistance (BPA) system for a small-scale vessel is addressed. A control-oriented model is derived from the physics underlying the system and gray-box identification is carried out by designing suitable experiments. A 3 DOF cascade control scheme is then implemented to achieve semi-automatic parking and station-keeping. The latter is also shown to be a solid groundwork for future research on fully automatic maneuver- ing. The proposed strategy is finally tested on stationkeeping and parking of a real vessel.

Keywords:Electrical power systems, Energy systems Abstract: We present a decomposition approach to a class of social welfare optimization problems for optimal power flow in multi-region electricity networks. The electricity network is decomposed into multiple regions which decide independently over the amount of power produced within the region and exchanged with neighboring regions. We decompose the overall power flow (or social welfare) optimization into region-based optimization problems (namely, power flow game), which is based on the introduction of dual variables representing nodal and link prices. Due to the interdependencies between regions' utilities, the social welfare maximizer might not necessarily correspond to a Nash equilibrium of the power flow game. We derive conditions under which the social welfare maximizer is a Nash equilibrium of the game, and investigate uniqueness of Nash equilibria. Finally, we examine whether convergence to the social welfare maximizer may occur under natural best-response dynamics.

Keywords:Electrical power systems, Game theoretical methods Abstract: Variability of supply is a fundamental difficulty associated with renewable resources in the electricity market. One way of mitigating this difficulty is to aggregate a diverse collection of resources in order to exploit the negative correlations that may exist among them. We consider a aggregation scheme where individual renewable energy producers offers day-ahead contracts to an aggregate manager which in turn participates in a two stage electricity market. The net payments received by the aggregate manager from the market have to be fairly distributed among the participants in the aggregate. Since the actual power supplied by the aggregate is random, its net payments are also random. The problem of sharing these random payments is complicated by the fact that different participants may have different statistical models for the payments because they have different statistical models for their (and other producers') net generation. We propose a simple payment sharing mechanism that is independent of the statistical models of the participants. We show that our payment sharing mechanism ensures that individual producers are better off in the aggregate than on their own. Further, under certain conditions, aggregation provides the social benefit of increasing the amount of renewable energy available in the day-ahead market.

Keywords:Electrical power systems, Linear systems Abstract: Regulation is a costly aspect of power system operation, which has long been inadequately and inconsistently incentivized via ill-formulated pricing schemes, as recently acknowledged by regulators. We propose a pricing formulation in which regulation prices are the optimal dual multipliers or costate of an optimal control problem. More precisely, we use the linear quadratic regulator to formulate a regulation pricing policy. We then construct a Vickrey-Clarke-Groves mechanism to induce honest participation among selfish agents. We apply the formulation to a scenario combining traditional frequency regulation and the California Independent System Operator's Flexible Ramping Product.

Keywords:Electrical power systems, Stochastic control, Decentralized control Abstract: In this paper, we propose a novel electricity dispatch and pricing mechanism that enables a grid with intermittent energy sources to dispatch energy within a user-specified risk bound in a decentralized manner. The key idea is to trade the standard deviation of future electricity supply and demand. A dispatchable power provider, such as a peaking power plant or a storage facility, adjusts its output in real time to reduce a certain amount of standard deviation of the future supply-demand balance. In the proposed market mechanism, such a dispatchable power provider can ``sell" the standard deviation at the price specified by a market. The market-clearing prices of the mean and the standard deviation of electricity are found through the Walrasian auction. This approach allows each power provider to specify the probability density function (pdf) of the amount of energy that it has to generate in the future. As a result, a power provider can quantitatively limit the risk of power shortage by imposing chance constraints in a decentralized manner. It can also evaluate the expected cost of future energy production as well as the cost of deviating its output by using the pdf. The decentralized risk-limiting dispatch and pricing problem are solved at each time step with a receding time horizon. We demonstrate the capabilities of the proposed approach by simulations using real data.

Keywords:Electrical power systems, Uncertain systems, Computational methods Abstract: Renewable energy sources often provide intermittent power at distributed locations in transmission and distribution networks. Efficient utilization of these sources must consider economics, computation, and reliability in managing network resources. A new computational tool for efficient dispatch of intermittent sources is developed using the risk limiting operational paradigm. Optimal dispatch of regulation and load following ancillary services is computed using current estimates of future random energy production. Substitution of intermittent power with firm power through a curtailment strategy is used to avoid regulation costs in excess of current firm power prices. The underlying mathematical framework is a non-convex optimal power flow problem, which is shown to have an exact convex relaxation under a set of realistic assumptions. The methodology is successfully tested on an IEEE 30-bus test system. Several operational effects of source uncertainty are captured. For instance, optimal solutions are shown to create power flows that mutually compensate intermittencies from different sources to minimize regulation requirements.

Keywords:Energy systems, Adaptive control, Stability of nonlinear systems Abstract: An adaptive control scheme for maximum power point tracking of a single-phase single-stage photovoltaic system connected to the grid is presented. The maximum power point depends on temperature and solar irradiance, ambient conditions that are time-varying and difficult to measure. Two solutions are presented. Each solution derive an estimator that approximate three different parameters. These parameters are functions of solar irradiance and temperature. In this manner, we eliminate the necessity of climatic sensors. The first solution, uses an adaptive estimator that is able to estimate constant parameters, and the second one uses a sliding mode estimator that is capable of estimate time-varying parameters. A complete analysis was done taking into account the nonlinearities showed by the closed-loop system. The Lyapunov redesign technique was used to derive a controller that gives globally asymptotically stable trajectories of the closed-loop system. Computer simulations are presented to compare the performance of both estimators and also to show the good performance of the controller.