Keywords: Biomedical systems, Linear time-varying systems, Identification for control
Abstract: We propose a method to identify diurnal changes in insulin action in patients suffering from type 1 diabetes mellitus (T1DM) based on data recorded by continuous glucose monitoring systems (CGMS). In order to do so the data is fitted using a continuous time transfer function including time dependent terms. The identified values for the insulin needs per gram of carbohydrate were compared with the patient-specific carbohydrate-to-insulin-ratios used for the calculation of the bolus insulin needs. A good agreement between the identified parameters and values determined by diabetologists were found. Furthermore, the diurnal variations in insulin action (as inferred from the changes in the patient-specific carbohydrate-to-insulin-ratios) could be reproduced. The identified models, including the diurnal changes in insulin action and the information on the intra-patient variability, have the potential to be used in future studies for managing the blood glucose level of patients, e.g. in a smart bolus calculator.

Keywords: Delay systems, LMI's/BMI's/SOS's, Biomedical systems
Abstract: Exogenous insulin administration is the standard way to regulate hyperglycemia in diabetic patients and, in the recent decades, the challenging task to design an artificial pancreas has been addressed with the aim to synthesize a closed-loop control law by means of sampled glucose measurements. Model-based control law allow to explicitly exploit the glucose-insulin mathematical model, but need to cope with different sources of uncertainties and disturbances affecting the system. The present note investigates the framework of the H_infty control as a tool to attenuate the effect of a meal, modeled as an unknown disturbance. To this end an LMI-based feedback control law is synthesized, by properly exploiting a Delay Differential Equation model of the glucose-insulin system, that makes use of only glucose measurements, to avoid the use of insulin measurements, known to be slower and more cumbersome to obtain, more expensive and also less accurate than glucose measurements. It is shown by simulations that, besides to regulate plasma glycemia onto a desired level starting from a hyperglycemic state, the control law efficiently constrains the post-prandial increase of glycemia on a very tight control, preventing dangerous oscillations.

Keywords: Metabolic systems, Modeling, Linear systems
Abstract: Nowadays, the requirements in the high quality managing and mathematical modeling of diabetes are increasing. Due to the several types of this chronic disease the problem represents a challenging task that was mostly covered in the literature for type 1 diabetes while examining algorithms for artificial pancreas. The aim of the current paper is to analyze a recently developed novel time-delay diabetes model elaborated for both type 1 and type 2 diabetes mellitus; hence, to handle mixed state of these diseases (double diabetes) as well. Control theoretical characteristics are investigated followed by parametric sensitivity analysis for both type 1 and type 2 cases. Finally, the model is compared with the well-known and widely used Cambridge (Hovorka)-model under different simulation scenarios.

Keywords: Uncertain systems, Biomedical systems
Abstract: The prediction of blood glucose for therapy optimization in type 1 diabetes has proved to be a difficult challenge. A main limitation is the presence of large intrapatient variability and hence, model uncertainty, which may jeopardize model individualization, both for data-based and physiological models. Interval models provide a natural framework to represent intra-patient variability in the form of interval parameters. Recent results have shown their potential in the context of glucose control, hypoglycemia risk prediction and fault detection. Interval-model-based methods rely on the prediction of envelopes containing all the possible glycemic responses according to the patient’s characterized intra-patient variability. Monotone systems theory has been successfully used for this purpose. Exact or tight glucose envelopes can be computed with mathematical guarantee and computational efficiency. A review of these methods is presented here with special focus on techniques to overcome the lack of monotonicity. The methods are illustrated with examples of different literature glucose-insulin models.

Keywords: Biomedical systems, Predictive control for linear systems, Reduced order modeling
Abstract: This paper presents a bihormonal artificial pancreas (AP) for people with type 1 diabetes (T1D) designed to provide a safe blood glucose control with minimal use of glucagon. The control algorithm uses insulin as well as glucagon to prevent hyper- and hypoglycemia. We employ a novel prediction-based activation of glucagon administration. The control algorithm consists of a Kalman filter, an insulin infusion model predictive controller (MPC), a proportional-derivative (PD) controller for glucagon infusion, and a meal time insulin bolus calculator. The PD controller is activated if the Kalman filter predicts hypoglycemia. Predictions utilize an ARMAX model describing glucose-insulin and glucose-glucagon dynamics. The model parameters are estimated from basic patient-specific data. A continuous glucose monitor provides feedback. We test the control algorithm using a simulation model with time-varying parameters available for 3 patients. We consider a simulation scenario where meals are estimated correctly as well as overestimated by 30%. The simulation results demonstrate that during normal operation, the controller only needs insulin and does not need glucagon. During unexpected events, such as insulin overdose due to an overestimated meal, the control algorithm uses glucagon efficiently to avoid severe hypoglycemia.

Keywords: Biomedical systems, Medical signal processing, Identification for control
Abstract: In this paper we estimate linear models for prediction of the interstitial glucose concentration in response to meals and bolus insulin. Parameters of these models can be directly used in simple bolus calculation rules. In contrast to models proposed in the literature, we present a model without an integrator. This model maintains the benefits of the existing empirical models and allows simulation of a longer time period than the post-prandial period, i.e. the couple of hours following a meal. Furthermore, the new model proposed in this paper does not require any re-initialization before meals.

Keywords: Distributed parameter systems, Stability of nonlinear systems, Nonlinear system theory
Abstract: This paper develops tools to construct Lyapunov functions establishing integral input-to-state stability (iISS) and input-to-state stability (ISS) for several classes of nonlinear parabolic equations. Using these constructions and an infinite-dimensional iISS small-gain theorem we provide a stability criterion for interconnections of iISS parabolic systems. We show that for interconnections of partial differential equations it is essential to choose right state and input spaces, especially for iISS subsystems which are not ISS.

Keywords: Fluid flow systems, Delay systems, Distributed parameter systems
Abstract: This work studies a convective flow system and presents experimental closed-loop results carried out on a test-bench representative of several industrial processes. This test bench consists of a horizontal column equipped with a mist actuator located at the inlet and fans generating an airvflow circulating along the tube. Following our recent theoretical design, we implemented a prediction-based control strategy aiming at stabilizing the mist at the output of the tube actuating on the wind speed. Correspondingly, this set-up involves a transport input-dependent delay (between the inlet and the output of the tube). We propose a control-oriented model, in which the transport delay satisfies an integral equation, and compared our prediction-based design with a conventional Proportional-Integral controller. Experimental results underline the relevance of the proposed approach.

Keywords: Observers for nonlinear systems, Distributed parameter systems, Process control
Abstract: In this paper, a simple observer design scheme is proposed for a class of 1-D semi-linear parabolic distributed parameter systems with in-domain measurement. The main idea of the design resides in imposing the measurement on the observer dynamics in a similar way as it is done in the finite-dimensional reduced order observer design. For the distributed system this is achieved through an additional algebraic constraint in the domain instead of an output injection mechanism. Correspondingly, the observer convergence is not induced by the correction scheme, but by the sensor location and the system parameters, and thus amounts on the underlying detectability property rather than the system observability. Possible applications to the case of unknown inputs are discussed. The proposed estimation approach is illustrated and tested through simulations with two representative examples: an unstable diffusive linear system with Dirichlet boundary conditions, and a stable isothermal single-species nonlinear tubular reactor with non-monotonic kinetics and Robin-Newman (i.e., Danckwerts) boundary conditions.

Keywords: Distributed parameter systems
Abstract: The approach recently proposed by the authors for the null controllability of 1-D parabolic equations is applied to the nontrivial case of a heat equation with discontinuous coefficients and subjected to Robin boundary conditions. The control steering the system to zero from a discontinuous initial state is comprehensively derived, together with the corresponding trajectory. Numerical experiments illustrate several features of the theory and demonstrate its effectiveness.

Keywords: Nonlinear system theory, Modeling, Maritime
Abstract: In this article, we study the Lagrangian controllablity of the Korteweg-de Vries (KdV) equation with the higher order velocity field for the N-solitons solution given in [4]. We prove that, for a given depth of the fluid h_0, there exists L_N>0 such that if L< L_N, then there exists a time T for which one can transport the fluid located in [0,L] to x>L. Physical applications of this result include the transportation of sediment and of polluted water.

Keywords: Stability of linear systems, Linear time-varying systems, Output feedback
Abstract: We consider the problem of boundary stabilization of 3 × 3 linear first-order hyperbolic systems with one positive and two negative transport speeds by using backstepping. The main result of the paper is to supplement the previous works how to choose muti-boundary feedback inputs applied on the state corresponding to the negative velocities to obtain finite-time stabilization of the original system in the spatial L2 sense. Our method is still valid for boundary stabilization of general n × n hyperbolic system with arbitrary numbers of states traveling in either directions.

Keywords: Predictive control for nonlinear systems, Computer aided control design, Optimization algorithms
Abstract: This paper provides a tutorial on the continuation/GMRES method (C/GMRES), which is a real-time optimization algorithm tailored for nonlinear model predictive control (NMPC) and a Maple version of AutoGenU, which is an automatic code generation system utilizing a symbolic computation language to simulate NMPC with C/GMRES. Once such settings of NMPC as the state equation and performance index are specified in a Maple worksheet, a problem-dependent C source file is automatically generated by symbolic computation, compiled, and executed. The worksheet also loads data files of simulation results and plots their time histories. This paper describes the usage and settings of AutoGenU for Maple.

Keywords: Automotive
Abstract: The oil crisis and strict emission legislation have greatly motivated the development of internal combustion engine technology. To improve fuel economy performance and reduce emissions, engine transient control has attracted wide research interests. However, engine system is a nonlinear physical plant with constraints on itself and actuators, and also it is a sophisticated control system involving many control loops to achieve single or multiple objectives. Therefore it is really a challenging issue on the transient control of the engine. In recent years, receding horizon control (RHC) was gained much attention in the field of engine control, owing to its advantages that it can explicitly tackle the constrained optimization and multi-variable control problem. However, a remarkable drawback of RHC is the heavy computation load for on-line optimization algorithm, especially for the nonlinear control system. Indeed, this bottleneck restricts its practical implementation on the industrial electronic controller of a fast control system for a long time. This tutorial paper proposes a systematic receding horizon controller design approach for the transient control applications of the gasoline engines. Two independent RHC-based tracking controllers aimed to achieve the engine torque and speed tracking control are designed, respectively. The control oriented model is derived from the mean-value model of gasoline engines, meanwhile the integrator of the tracking error is embedded to improve the tracking accuracy. All the proposed controllers are verified in real-time on a full-scale gasoline engine and the on-line optimization algorithm for RHC adopts C/GMRES method, which can provide an approximately optimal solution by solving the linear equation instead of the Riccati differential equation. The experimental results demonstrate a large potential for improving the engine transient control performance with RHC scheme.

Keywords: Predictive control for nonlinear systems, Automotive, Optimal control
Abstract: This paper proposes an optimal control approach to control systems described by discrete time I/O models. In particular, the C/GMRES method, which is a curse-ofdimensionality free and fast approximative optimal control method is adapted to this purpose. Comparing this approach with conventional industry standard methods, the benefits are twofold: First, easy and intuitive tuning of the control via the quadratic cost function of the optimization problem, reducing the necessary parameterization and tuning effort typical in industrial applications. Second, direct use of discrete time I/O models, typically the result of data based modeling efforts, which themselves can reduce development time drastically, compared to classical first principles and parameterization methods. To demonstrate the possible advantages of this method, it is applied to a problem, where tedious control parametrization and the resulting tuning efforts are state of the art: The control of the Diesel Engine Air-Path is a MIMO system tracking problem, where the achieved tracking error of the outputs are decisive of the main emissions of the Diesel Engine, which are NOx and Soot.

Keywords: Automotive, Predictive control for nonlinear systems, Transportation systems
Abstract: Ecological (eco)-driving aims at improving fuel efficiency of a vehicle by taking smooth driving action in the road traffic networks. This paper presents an advanced eco-driving system for a host vehicle that uses information of surrounding vehicles, road gradients and the state of upcoming traffic signals to predict the future traffic states using the dynamical models, and based on the predicted information it generates the optimal vehicle control inputs in a model predictive control framework. The control objective is considered to maximize fuel economy by regulating a safe headway distance or cruising at the optimal velocity under bounded driving torque condition. A fast optimization technique using continuation and generalized minimum residual (C/GMRES) method is used in the framework for real-time optimization of control inputs. The proposed eco-driving system is evaluated in highly interactive urban traffic using the microscopic traffic simulator Aimsun, and its performance is compared with the traditional driving system.

Keywords: Automotive, Predictive control for nonlinear systems
Abstract: This paper is a tutorial for a path generation method during merging maneuver of automobile using a model predictive control scheme. Lanes of a motor way are approximated with proposed smooth lines. Assuming that the main lane vehicles run on the centerline of the main lane, an appropriate path of the merging vehicle can be simply designed and modified according to the motion of the main lane vehicles. A computer simulation of the merging maneuver of one merging vehicle and two main lane vehicles using actual merging data is conducted.

Keywords: Automotive, Predictive control for nonlinear systems, Optimization
Abstract: This paper presents the design of a model predictive controller for Diesel engine air-path system that coordinates the actuators of a two-stage turbocharger to reduce the aftertreatment warm-up time, optimizing the boost pressure and maintaining the desired EGR ratio.

Starting from a control-oriented model of the engine air-path system, a bypass valve thermal model is derived to predict the temperature at the inlet of the Diesel Oxidation Catalyst. Then, a discrete-time piecewise affine system is obtained by combining the linearized model at different operating points. The rapid warm-up control problem is formulated as a tracking problem and solved by applying Model Predictive Control. The effects of different weights in cost function are evaluated to elucidate the trade-off between boost pressure and warm-up performance. Finally, a heuristic control for rapid warm-up is developed from the analysis of the simulation results with MPC.

Keywords: Linear parameter-varying systems, Automotive, H2/H-infinity methods
Abstract: In this paper, we present a motion-scheduled LPV/Hinf suspension controller that takes into account the three main motions of the vehicle vertical dynamics: bounce, roll and pitch motions. The new approach aims, by using a motion detection method, at designing a controller which is able to adapt the suspension forces at the four corners of the vehicle, in order to mitigate the road-induced effects. The motion detection strategy is based on the supervison of load transfer distributions (pitch and roll motions). The main idea of the LPV control is to use three scheduling parameters, representative of the motion distribution of the car dynamics, in order to adapt and distribute efficiently the suspension actuators. A full 7 degree of freedom (DOF) vertical model is used to describe the body motion (chassis and wheels) and to synthesize the LPV controller. The controller solution, derived in the LPV/Hinf framework, is based on the LMI solution for polytopic systems. Some simulation results are presented that show the effectiveness of this approach.

Keywords: Automotive, Game theoretical methods, Adaptive control
Abstract: This paper introduces an adaptive approach for a game-theoretic strategy on Complete Vehicle Energy Management. The proposed method enhances the game-theoretic approach such that the strategy is able to adapt to real driving behavior. The classical game-theoretic approach relies on one probability distribution function whereas the proposed approach is made adaptive by using dedicated probability distribution functions for different drive patterns. Owing to the adaptability of the proposed approach, the strategy is further refined by proposing dedicated objective functions for the driver player and for the auxiliary player. Next, an algorithm is developed to classify the measured driving history into one of the pre-defined drive pattern and employ the corresponding game-theoretic strategy. Multiple strategies are simulated with a model of a parallel hybrid heavy-duty truck with a battery and electric auxiliaries. The fuel reduction results are compared and the adaptive game-theoretic approach shows an improved and a more robust performance over different drive-cycles compared to the non-adaptive one.

Keywords: Automotive, Transportation systems, Optimal control
Abstract: The aim of this work is, while using an optimal approach with dynamic programming (DP), to determine the best eco-driving cycle starting from a given driving cycle. To find the cycle with the minimum fuel consumption, two ways of computing an eco-driving cycle are compared. For a Hybrid Electric Vehicle (HEV), is it more efficient to compute an HEV based eco-driving cycle or to compute a conventional vehicle based eco-driving cycle and then to adapt it to a hybrid vehicle? Hence, two different DP programs are developed, that lead to two different eco-driving cycles: hybrid and conventional. Finally, the fuel consumption of an HEV with two Energy Management Strategies (EMS) will be compared: an off-line optimal one based on the Pontryagin Minimum Principle and an on-line suboptimal Equivalent Consumption Minimization Strategy (ECMS). The paper shows that in order to generate the best speed trajectory in terms of fuel consumption, it is necessary to take the fact that the vehicle is an HEV into account.

Keywords: Automotive, Optimization, Predictive control for linear systems
Abstract: In this paper, a switching Model Predictive Control strategy is proposed for a Waste Heat Recovery system in heavy-duty automotive application. The objective is to maximize the WHR system output power while satisfying the output constraints under highly dynamic engine variations. For control design, a WHR system architecture with the expander and pumps decoupled from the engine is considered. Compared to a WHR system with the expander coupled to the engine, up to 29% more output power is obtained for the considered design. This holds for both steady state and highly dynamic engine conditions. The simulation results are obtained using a validated high-fidelity WHR system model with realistic disturbances from a Euro VI heavy-duty diesel engine.

Keywords: Automotive, Optimal control
Abstract: Since the last decade, hybrid electric vehicles (HEVs) have been and are introduced increasingly by automotive industry as they provide substantial improvements in fuel consumption. However, the optimal power distribution between the different energy sources in a HEV to achieve high efficiency is a non trivial problem. In a former work, an approximate solution to the generic optimization task by a two-stage approach based on LP and switching strategies was introduced, which is extended within this work. First, the opportunity to declutch and switch off the combustion engine is considered, which extends the LP to a MILP and allows additional improvements in fuel consumption. The second extension introduces a receding horizon strategy which considers the current SOC of the battery and a target SOC at the end of the horizon during the top level optimization. Thus a complete knowledge of the driving cycle is not required but only a prediction for a shorter horizon. Furthermore, errors caused by model plant mismatch and prediction can be compensated by the SOC feedback. Both extensions result on a minimum increase in computational effort and allow to formulate the optimization as LP/MILP and solve it by real-time capable solvers. As application example a parallel HEV model with the opportunity to declutch the ICE and including a realistic powertrain and battery model is considered. The method and the proposed extensions were evaluated in simulation and experimental where satisfactory results could be achieved in both cases.

Keywords: Nonlinear system theory, Lyapunov methods, Stability of nonlinear systems
Abstract: In this paper, the problem of stabilization of bilinear control systems is considered. Based on the technique of linear matrix inequalities and quadratic Lyapunov function, the so-called stabilizability ellipsoid is designed, such that the trajectory of the closed-loop system, starting inside the ellipsoid asymptotically tends to zero. The results obtained allow to design an approximation of the stabilizability domain of the bilinear control system.

Keywords: Nonlinear system theory, Lyapunov methods, Stability of nonlinear systems
Abstract: This communication deals with a long standing open problem in the field of multidimensional systems. We tackle the question of the existence and uniqueness of the solutions for nonlinear continuous 2D Roesser models. It is proved that if the function describing the Roesser model is globally Lipschitz, a continuous solution exists and is unique for a given set of initial conditions. Several examples show that these assumptions cannot be easily relaxed. This is an important basis that is crucial to the analyzes of stability and stabilization of nonlinear Roesser models.

Keywords: Nonlinear system theory, Predictive control for nonlinear systems, Stability of nonlinear systems
Abstract: In this paper, a nonlinear continuous-time dynamics with input-delay is considered. Assuming the existence of a continuous-time stabilizing strategy in the delay free case, it is shown how the problem can be recasted in the sampled-data context as an Immersion and Invariance stabilizing one. Conditions ensuring stabilization of the input-delayed dynamics at the sampling instants are given. Examples conclude the paper.

Keywords: Nonlinear system theory, Stability of nonlinear systems, Robotics
Abstract: A virtual holonomic constraint (VHC) is a relation among the generalized coordinates of a mechanical system that can be made invariant via feedback control. The autonomous dynamics of the system resulting on the enforcement of the VHC are called the constraint dynamics. This work presents a method for the synthesis of VHCs that guarantees the existence of an asymptotically stable limit cycle on the constraint dynamics.

Keywords: Nonlinear system theory, Stability of nonlinear systems
Abstract: This paper deals with a robust synchronization problem for multistable systems evolving on manifolds in the context of Input-to-State Stability (ISS) framework. Based on a recent generalization of classical ISS theory to multistable systems (may have unstable equilibrium), a robust synchronization protocol is designed with respect to a compact invariant set of the unperturbed system. The invariant set is assumed to admit a decomposition without cycles (basically no homoclinic nor heteroclinic orbits may exist). Numerical simulation examples illustrate our theoretical results.

Keywords: Network analysis and control, Agents networks
Abstract: In this paper, we study the translational and rotational (SE(N)) invariance properties of locally interacting multi-agent systems. We focus on a class of networked systems, in which the agents have local pairwise interactions, and the overall effect of the interaction on each agent is the sum of the interactions with other agents. We show that such systems are SE(N)-invariant if and only if they have a special, quasi-linear form. The SE(N)-invariance property, sometime referred to as "left invariance", is central to a large class of kinematic and robotic systems. When satisfied, it ensures independence to global reference frames. In an alternate interpretation, it allows for integration of dynamics and computation of control laws in the agents' own reference frames. Such a property is essential in a large spectrum of applications, e.g., navigation in GPS - denied environments. Because of the simplicity of the quasi-linear form, this result can impact ongoing research on design of local interaction laws. It also gives a quick test to check if a given networked system is SE(N)-invariant.

Keywords: Agents networks, Concensus control and estimation, Control over networks
Abstract: This work is concerned with the controllability of the single-leader multi-agent system with the chain structures. It is shown that the multi-chain system evolving according to the consensus policy described by the linear time-invariant model is controllable if and only if the system does not have two chain lengths satisfying some specific pattern. This result improves a recent elegant work on the similar topic, where only a sufficient condition for the system uncontrollability was proposed.

Keywords: Agents networks, Concensus control and estimation, Control over networks
Abstract: In this paper, we apply the recently developed technique for collective motion of a multi agent system (MAS) [1-10] to transform a multi unicycle-like robot system as particles of a continuum deformation under a homogenous mapping. For this purpose, the proposed leader-follower model is applied and first a desired homogenous mapping is formulated based on the trajectories chosen by three leader agent where they remain non-aligned at any time 􀢚 during evolution. Then, every follower agent is allowed to acquire the desired homogenous mapping through local communication and update its centroid position based on the centroid positions of the three neighboring agents where communication weights are uniquely determined based on initial distribution of the agents. Therefore, multi unicycle robot system move collectively from a given initial formation to a desired final region where (i) collision of agents with obstacles can be avoided by choosing proper trajectories for the leaders, and (ii) the area occupied by the MAS can be largely expanded or contracted.

Keywords: Agents networks, Concensus control and estimation, Linear systems
Abstract: The main objective of the synchronization of multi-agent systems is the asymptotic convergence of the agents towards a common trajectory. For practical purposes, it is required that the transient behavior of the synchronization errors satisfies additional criteria, such as requirements on a maximum settling time or a minimum damping. In this paper, it is first analyzed how these specifications on the the synchronization errors can be related to the parameters of the networked system. Secondly, a design method for synchronizing dynamic controllers is presented that ensures the requirements on the networked multi-agent system for arbitrary bidirectional interconnections. The results are demonstrated by its experimental application to the synchronization of the lateral dynamics of mobile robots.

Keywords: Agents networks, Concensus control and estimation
Abstract: In this paper, we study the asymptotic behaviors of threshold models used to describe the formation of collective actions in social networks. At each time instant, each agent of the network makes a choice between two possible actions. The decision is made on the basis of the actions chosen by its neighbors and the value of a dynamically updated threshold. The main novelty of the proposed model is the introduction of a parameter accounting for the level of self-confidence of the agents, which affects the dynamic evolution of the threshold and in turn the way the agents make their decision. The objective is to identify which are the possible limiting behaviors of the network and under which conditions each of them occurs. Three different network topologies are considered. In the case of complete graph, the asymptotic behaviors are analytically characterized, whereas for star and ring graphs an extensive numerical analysis is presented.

Keywords: Agents networks, Distributed cooperative control over networks, Agents and autonomous systems
Abstract: This paper discusses generalized controllers for rigid formation shape stabilization. We provide unified analysis to show convergence using different controllers reported in the literature, and further prove an exponential stability of the formation system when using the general form of shape controllers. We also show that different agents can use different controllers for controlling different distances to achieve a desired rigid formation, which enables the implementation of heterogeneous agents in practice for formation shape control. We further propose an event-triggered rigid formation control scheme based on the generalized controllers. The triggering condition, event function and convergence analysis are discussed.

Keywords: Electrical power systems, Energy systems, Decentralized control
Abstract: An optimal decentralized control approach for damping of inter-area oscillations in power systems with a guaranteed level of damping is suggested in this paper. Wide-area signals are used to supplement the actions of local controllers to improve the damping of the overall system. To guarantee a well-damped transient response, poles of the closed-loop system are required to be in a prescribed region. To optimize the performance of the system, the standard quadratic performance index is considered and minimized. A heuristic iterative algorithm is proposed which allows simultaneous design of the control structure and the control gain. At the same time, regional pole-placement constraints are taken into account and thereby a prescribed level of damping is guaranteed. The control structure and the control gain are designed by minimizing the number of required communication links and maximizing the closed-loop performance. The approach also allows promoting a pre-specified fixed-structure decentralized control design. The method is demonstrated on a two-area four-machine benchmark and the results shows the effectiveness of the method and robustness of the design to delays and parametric uncertainties.

Keywords: Electrical power systems, Energy systems, Modeling
Abstract: The synchronisation of generators is one of the most sophisticated control problems in electrical power systems. In publications from the field of system theory, Non-Uniform Kuramoto Oscillators has been suggested as an appropriate tool for analysing this problem. The authors of this publication have a background in power engineering and have applied the suggested methodology to a benchmark problem. The paper presents the application and results and argues the applicability of the methodology from a power systems point of view.

Keywords: Electrical power systems, Linear systems, Filtering
Abstract: This paper studies a state estimation problem for a networked dynamic system characterized by a communication graph. A new distributed state estimation method is based on a distributed MAP (maximum {em a posteriori}) estimation algorithm for each node to update its local state. This distributed method is applied to the state estimation problem for a large power network and illustrated using the IEEE 118-bus system. It is shown that the performance of this method is close to that given by a centralized Kalman filtering approach and much better than that given by a local Kalman filtering approach, yet the computational complexity and communication load of the proposed method are low for each node, making the method scalable for large-sized networked systems.

Keywords: Electrical power systems, Optimal control, Uncertain systems
Abstract: We address an optimal control problem for a microgrid in islanded operation with bounded uncertain load and renewable infeed. While model predictive control (MPC) with worst-case cost evaluation is often employed to obtain robust optimal control laws in the presence of bounded disturbances, it suffers from an inherent conservativeness. To counteract this phenomenon, we propose an approximate closed-loop minimax MPC scheme, where the renewable energy sources output can be curtailed. The MPC is formulated as a mixed-integer linear program, solved online and applied in a receding horizon fashion. In the case study, the approximate closed-loop approach yields a better prediction accuracy and performance than the corresponding open-loop scheme

Keywords: Electrical power systems, Optimization, Uncertain systems
Abstract: Large-scale penetration of photovoltaic (PV) power generators and storage batteries is expected into the power system in Japan. To maintain the supply-demand balance with energy storage, the optimal power generation and the charge/discharge power of storage batteries can be determined in a manner of the model predictive control of generators. In view of this, this paper addresses a problem of the day-ahead scheduling for the supply-demand-storage balance with explicit consideration of the model predictive power generation. This scheduling is performed by using demand prediction, whose uncertainty is expressed in terms of interval prediction. Formulating the day-ahead scheduling problem as an interval-valued allocation problem, we give a solution to it by taking an approach based on the monotonicity analysis with respect to the optimal solution. Finally, the efficiency of the proposed method is verified through a numerical simulation, where we use an interval prediction of PV power generation constructed by experimental data.

Keywords: Electrical power systems, Distributed control, Stability of nonlinear systems
Abstract: Recently sum-of-squares (SOS) based methods have been used for the stability analysis and control synthesis of polynomial dynamical systems. This analysis framework was also extended to non-polynomial dynamical systems, including power systems, using an algebraic reformulation technique that recasts the system's dynamics into a set of polynomial differential algebraic equations. Nevertheless, for large scale dynamical systems this method becomes inapplicable due to its computational complexity. For this reason we develop a subsystem based stability analysis approach using vector Lyapunov functions and introduce a parallel and scalable algorithm to infer the stability of the interconnected system with the help of the subsystem Lyapunov functions. Furthermore, we design adaptive and distributed control laws that guarantee asymptotic stability under a given external disturbance. Finally, we apply this algorithm for the stability analysis and control synthesis of a network preserving power system.

Keywords: Markov processes, Stochastic control, Stochastic systems
Abstract: Several well-known algorithms in the field of combinatorial optimization can be interpreted in terms of the primal-dual method for solving linear programs. For example, Dijkstra's algorithm, the Ford-Fulkerson algorithm, and the Hungarian algorithm can all be viewed as the primal-dual method applied to the linear programming formulations of their respective optimization problems. Roughly speaking, successfully applying the primal-dual method to an optimization problem that can be posed as a linear program relies on the ability to find a simple characterization of the optimal solutions to a related linear program, called the `dual of the restricted primal' (DRP).

This paper is motivated by the following question: What is the algorithm we obtain if we apply the primal-dual method to a linear programming formulation of a discounted cost Markov decision process? We will first show that a widely-used variant of the value iteration algorithm for Markov decision processes can be interpreted in terms of the primal-dual method, where the value function is updated with suboptimal solutions to the DRP in each iteration. We then provide the optimal solution to the DRP in closed-form, and present the algorithm that results when using this solution to update the value function in each iteration. Unlike the algorithms obtained from suboptimal DRP updates, this algorithm is guaranteed to yield the optimal value function in a finite number of iterations. Finally, we show that the iterations of the primal-dual algorithm can be interpreted as repeated application of the policy iteration algorithm to a special class of Markov decision processes. When considered alongside recent results characterizing the computational complexity of the policy iteration algorithm, this observation could provide new insights into the computational complexity of solving discounted-cost Markov decision processes.

Keywords: Modeling, Computational methods, Sensor and signal fusion
Abstract: Source estimation is a fundamental ingredient of Full Waveform Inversion (FWI). In such seismic inversion methods wavelet intensity and phase spectra are usually estimated statistically although for the FWI formulation as a nonlinear least-squares optimization problem it can naturally be incorporated to the workflow. Modern approaches for source estimation consider robust misfit functions leading to the well known robust FWI method. The present work uses synthetic data generated from a high order spectral element forward solver to produce observed data which in turn are used to estimate the intensity and the location of the point seismic source term of the original elastic wave PDE. A min-max filter approach is used to convert the original source estimation problem into a state problem conditioned to the observations and a non-standard uncertainty description. The resulting numerical scheme uses an implicit midpoint method to solve, in parallel, the chosen 2D and 3D numerical examples running on an IBM Blue Gene/Q using a grid defined by approximately sixteen thousand 5th order elements, resulting in a total of approximately 6.5 million degrees of freedom.

Keywords: Agents and autonomous systems, Autonomous robots, Cooperative control
Abstract: This paper is concerned with the development of motion safety criteria and associated proofs of safe operation for the class of reciprocal collision avoidance methods based on the relative velocity paradigm; including Velocity Obstacles (VO), Reciprocal Velocity Obstacles (ORCA), and Continuous Control Obstacles (CCO).

In the first part of this paper various notions of safety are reviewed and formalized, beginning with the most stringent of definitions which are then gradually relaxed while retaining practical applicability. In the second part of the paper, the developed safety notions are applied to the specified class of relative velocity-based reciprocal collision avoidance methods for which no guarantees for safe operation were known before. We develop a set of partial results, which, when incorporated into the individual collision avoidance routines, provably lead to safe and collision-free overall operation.

Keywords: Sliding mode control, Observers for linear systems, Optimal control
Abstract: The problem of the sliding mode control design is considered for the LTI system with multiplicative disturbances of the input and the noisy measurements of the output. The minimax observer is designed in order to provide the best possible estimate of the system's state. The problem of optimal reaching (as close as possible) of the selected sliding surface is the studied and sub-optimal control algorithms which generate continuous and discontinuous feed-back controls are presented. The theoretical results are illustrated by an academic example.

Keywords: Statistical learning, Electrical power systems, Energy systems
Abstract: With increasing penetration of solar and wind energy to the total energy supply mix, the pressing need for accurate energy forecasting has become well-recognized. Here we report the development of a machine-learning based model blending approach for statistically combining multiple meteorological models for improving the accuracy of solar/wind power forecast. Importantly, we demonstrate that in addition to parameters to be predicted (such as solar irradiance and power), including additional atmospheric state parameters which collectively define weather situations as machine learning input provides further enhanced accuracy for the blended result. Functional analysis of variance shows that the error of individual model has substantial dependence on the weather situation. The machine-learning approach effectively reduces such situation dependent error thus produces more accurate results compared to conventional multi-model ensemble approaches based on simplistic equally or unequally weighted model averaging. Validation over an extended period of time results show over 30% improvement in solar irradiance/power forecast accuracy compared to forecasts based on the best individual model.

Keywords: Concensus control and estimation, Cooperative autonomous systems, Distributed cooperative control over networks
Abstract: We present a convergence result for a non-homogeneous Markov chain that arises in the study of networks employing the additive-increase multiplicative decrease (AIMD) algorithm. We then use this result to solve the network utility maximization (NUM) problem.

Keywords: Optimization algorithms, Lyapunov methods, Optimization
Abstract: The estimation of the Domain of Attraction (DA)is an important topic in investigation of system stability. Using Lyapunov’s conditions leads to a dependency of the chosen Lyapunov function and the size of the estimation. This paper presents a method, which delivers the coefficients of the optimal quadratic Lyapunov function (OQLF) for a given system. Additionally the method determines the largest estimation of the DA. Therefore, the coefficients of the quadratic Lyapunov function are intervals. The coefficients are optimized by an iteratively outer optimization algorithm based on interval arithmetic. An inner optimization algorithm delivers an estimation for the DA’s size of all QLF which can be constructed from the coefficient intervals. This yields the largest estimation of the DA as well as OQLF for the given system.

Keywords: Optimization algorithms, Optimization, Distributed control
Abstract: In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we show that under the assumption that the Hessian of the primal objective function is bounded we have a global error bound type property for the dual problem. Using this error bound property we devise a fully distributed dual gradient scheme for which we derive global linear rate of convergence. The proposed dual gradient method is fully distributed, requiring only local information, since is based on a weighted stepsize. Our method can be applied in many applications, e.g. distributed model predictive control, network utility maximization or optimal power flow.

Keywords: Optimization, Optimization algorithms
Abstract: This paper establishes global convergence and provides global bounds of the rate of convergence for the Heavy-ball method for convex optimization. When the objective function has Lipschitz-continuous gradient, we show that the Ces{'a}ro average of the iterates converges to the optimum at a rate of mathcal{O}(1/k) where k is the number of iterations. When the objective function is also strongly convex, we prove that the Heavy-ball iterates converge linearly to the unique optimum. Numerical examples validate our theoretical findings.

Keywords: Optimization, Optimization algorithms
Abstract: This paper investigates the battery charging schedule problem of a battery-swapping station for electric buses (EB). An EB assignment policy is proposed such that there is a one-to-one correlation between EBs and batteries. By this means, the battery charging schedule problem aiming to minimize the total cost of the battery-swapping station is formulated as a constrained convex program with both spatially and temporally coupled constraints. Based on dual decomposition and our proposed EB assignment policy, the battery charging schedule problem can be decomposed into a series of local subproblems, which can be independently tackled. Furthermore, a fast search method in combination with binary search is put forward to deal with subproblems. Therefore, the battery charging schedule problem can be solved efficiently in a distributed manner. Numerical results confirm the validity of our proposed approach.

Keywords: Optimization algorithms, Game theoretical methods, Transportation systems
Abstract: We consider the problem of imputing the function that describes an optimization or equilibrium process from noisy partial observations of nearly optimal (possibly non- cooperative) decisions. We generalize existing inverse optimiza- tion and variational inequality problems to construct a novel class of multi-objective optimization problems: approximate bilevel programs. In this class, the “ill” nature of the comple- mentary condition prevalent in bilevel programming is avoided, and residual functions commonly used for the design and analysis of iterative procedures, are a powerful tool to study approximate solutions to optimization and equilibrium prob- lems. In particular, we show that duality gaps provide stronger bounds than lp norms of KKT residuals. The weighted criterion method is in some sense equivalent to existing formulations in the case of full observations. Our novel approach allows to solve bilevel and inverse problems under a unifying framework, via block coordinate descent, and is demonstrated on 1) consumer utility estimation and pricing and 2) latency inference in the road network of Los Angeles.

Keywords: Optimization, Optimal control, Optimization algorithms
Abstract: Additively weighted Voronoi diagram and weighted Delaunay decomposition are a generalization of Voronoi diagram and Delaunay triangulation, respectively. They have received much attention due to their relevance in many domains see [1], [2], [3]. In particular, their interest in control theory has been recently shown in [4], [5] to solve inverse parametric linear/quadratic programming problem. This paper elaborates on the identification of suitable sites and weights of such particular partitions via two algorithms. It will be shown that these algorithms require solving a bi-linear programming problem.

Keywords: Reduced order modeling, Identification, Delay systems
Abstract: An algorithm for the estimation of the moments of linear systems and linear time-delay systems from input/output data is proposed. The estimate, which converges to the moments of the system, is exploited to construct a family of reduced order models. These models asymptotically match the moments of the unknown system to be reduced. The computational complexity of the algorithm is analyzed and the use of the algorithm is illustrated by a benchmark example.

Keywords: Model/Controller reduction, Reduced order modeling, Linear systems
Abstract: In this paper we study the problem of computing the (family of) reduced order model(s) that satisfy the following properties: the systems match the moments of the given to be reduced system and the same holds for the first order derivatives of the corresponding transfer functions. We prove that such a model exists and compute it. We also study the problem of moment matching for the state-space representations of the first order derivatives of rational transfer functions. Finally, we show that the model that matches the moment of both the given system and its first order derivative is a member of the family of reduced order models whose first order derivatives achieve moment matching.

Keywords: Reduced order modeling, Large-scale systems, Complex systems
Abstract: The study of methods that involve rational interpolation is of interest. We provide an overview of the Loewner framework which is interpolatory but uses measured or computed data (e.g. measurements of the frequency response of a to-be approximated system) instead of the system matrices, and constructs reduced models based on a rank revealing factorization of appropriately constructed matrices. We concentrate on generalizing the already existing framework for linear to bilinear and quadratic bilinear systems. The primary reason behind using quadratic bilinear systems is that they represent the bridge between linear and nonlinear systems. For certain types of nonlinear systems, we can always find an equivalent quadratic bilinear model without performing any approximation.

Keywords: Computational methods, Large-scale systems, Linear systems
Abstract: Uncertainties in mathematical models are often represented by stochastic parameters. We consider high dimensional single-input single-output (SISO) systems whose system matrices have affine dependencies on stochastically uncorrelated parameters. We introduce a reformulated SISO system for the mean the stochastic output of the original parametric system. The problem is reformulated using tensors, represented in low-rank format. A two-sided tensor Arnoldi method is used for model order reduction of the high dimensional formulation. This results in a reduced model for the mean that is compared to the parametric reduced model that results from classical parametric model reduction.

Keywords: Model/Controller reduction, Large-scale systems, Delay systems
Abstract: In this paper, the problem of determining the approximate stability regions of large-scale time-delay systems (LS TDS) is solved using model approximation techniques. To achieve this, an mathcal{H}_2-oriented approximation algorithm, referred to as textbf{TF-IRKA}~cite{beattie2012realization}, is considered. This algorithm has been shown to be well suited for the approximation of infinite-dimensional systems into finite-dimensional ones. We show here how model reduction can be used to approximate time-delay systems with multiple delays and obtain a fairly accurate estimation of their stability regions. Discussions regarding the adaptation of existing algorithms to the considered problem are also provided. Several numerical examples illustrate the efficiency and accuracy of the approach.

Keywords: Model/Controller reduction, Computational methods, Distributed parameter systems
Abstract: We survey several algorithm for H2 optimal model reduction with a particular emphasis on the case of approximating irrational functions. Irrational transfer functions arise for systems modeled by partial differential equations or delay differential equations. We then compare the performance of these algorithms on two examples of irrational transfer functions: one arising from a heat equation and one arising from a beam equation.

Keywords: Neural networks, Adaptive control, Complex systems
Abstract: This paper deals with the adaptive control of single-input multi-output (SIMO) underactuated nonlinear systems. The restriction of the control authority for these systems causes major difficulties in control design. In this work, we propose an adaptive neural controller based on neural emulator to solve the control problems for a class of SIMO nonlinear systems. This controller is built by a set of partial neural controllers. New formulas are proposed to compute the validity degrees which manage the generation of the global control law. Simulations are carried out on a single-input multi-output nonlinear system. The obtained results show that the suggested control scheme provides a very good tracking and regulation performance.

Keywords: Neural networks, Optimal control, Game theoretical methods
Abstract: A novel time-based finite-horizon near optimal design is proposed for nonlinear two-player zero-sum games with completely unknown system dynamics. First, an online Neural Network (NN) identifier is developed to learn the dynamics of the nonlinear continuous-time system. Then, a novel online NN-based approximator is proposed to estimate the time-varying solution, referred to as value function, of the Hamilton-Jacobi-Isaacs (HJI) equation in a forward-in-time manner. Subsequently, by utilizing the estimated time-varying value function from the NN-based approximator and system dynamics from the online NN identifier, the near optimal strategies for nonlinear two-player zero-sum game are derived. To deal with time varying property of the value function, a NN structure with constant weights and time-varying activation functions are considered and a suitable NN update law is proposed based on normalized gradient descent approach. In order to ensure the stability and to satisfy terminal cost at the fixed final time, two novel additional terms, one corresponding to terminal cost, and the other to stabilize the nonlinear two-player zero-sum game are introduced to the update law of the NN-based approximator. Standard Lyapunov theory is utilized to verify the uniformly ultimately boundedness of the closed-loop system. Simulation results demonstrate the effectiveness of the proposed scheme.

Keywords: Neural networks, Power electronics, Adaptive systems
Abstract: In this paper, an adaptive neural backstepping controller (ANBC) is proposed for three- phase active power filter (APF). An adaptive neural controller is developed to deal with the nonlinear APF system using backstepping method, improving the current tracking and increasing the power quality. The proposed radial basis function (RBF) neural network (NN) whose weights are adjusted online by the adaptive law is designed to approximate the nonlinear function of APF model. The proposed ANBC can realize the desired dynamic behavior and improve the robustness of the APF system. Simulations using MATLAB /SimPower Systems Toolbox demonstrate the high performance of the proposed adaptive neural backstepping control strategy.

Keywords: Stability of nonlinear systems, Output feedback, Fuzzy systems
Abstract: This paper is to propose a systematic method for the design of a dynamic output feedback controller for nonlinear systems in Takagi-Sugeno form subject to input saturation. The proposed method is based on a new technique for modeling the saturation effect that allows taking its nonlinearity effects into the problem of controller design. Based on Lyapunov theory, sufficient conditions for ensuring the system global stability are formulated in terms of linear matrix inequalities (LMIs) considering the -gain performance specification under amplitude bounded exogenous disturbances. An example is presented to illustrate the effectiveness of the proposed method.

Keywords: Fuzzy systems
Abstract: Linear controller design can be carried out for nonlinear systems e. g. by using Takagi-Sugeno fuzzy models. With such an approximative design via linearization in several approximation points, when designing a controller in a transient region, drift terms occur. These are frequently neglected during controller design. An approach for approximative compensation of these drift terms by the control law is proposed in this work which leads to a locally linear/affine parallel distributed controller design. The novel method is demonstrated on the benchmark problem of an inverted pendulum.

Keywords: Sampled data control, Constrained control, LMI's/BMI's/SOS's
Abstract: This paper addresses the problem of stability analysis of sampled-data control of linear systems in the presence of magnitude and rate saturation. A position-type feedback modeling for the actuator is considered. Based on the use of a discrete-time quadratic Lyapunov function, a looped-functional and generalized sector relations (to cope with nested saturation functions), LMI conditions are derived to assess local (regional) and global stability of the sampled-data closed-loop systems under aperiodic sampling strategies. These conditions are then incorporated in convex optimization problems aiming at maximizing estimates of the region of attraction of the origin or maximizing the inter-sampling time for which the stability is ensured regionally or, when possible, globally.

Keywords: Sampled data control, Delay systems, Cooperative autonomous systems
Abstract: The goal of this paper is to compute transmission rates and delays that provably stabilize Multi-Agent Systems (MASs) in the presence of disturbances and noise. In other words, given the existing information delay among the agents and the underlying communication topology, we determine rates at which information between the agents need to be exchanged such that the MAS of interest is Lp-stable with bias, where this bias accounts for distorted/noisy data. In an effort to consider MASs characterized by sets of equilibrium points, the notions of Lp-stability (with bias) and Lp-detectability with respect to a set are utilized. Using Lyapunov-Razumikhin type of arguments, we are able to consider delays that are greater than the transmission intervals. The present methodology is applicable to general (not merely to single- and double-integrator) heterogeneous linear agents, directed topologies and output feedback. The computed transmission rates are experimentally verified employing a group of off-the-shelf quadcopters.

Keywords: Sampled data control, Emerging control applications, Modeling
Abstract: The article proposes a hypothetico-inductive approach to the formulation of suitable thermal zones, for subsequent multi-zone modelling and spatial control of microclimatic variables in buildings. Here, model structures are initially identified from data, thus avoiding undue reliance on prior hypotheses and ensuring that the resulting models are fully identifiable from the available temperature measurements. More specifically, an agglomerative hierarchical clustering approach is used to quantitatively distinguish and group thermal zones within an open airspace for any given ventilation and heating combination. To evaluate the new approach, the article utilises a previously developed Hammerstein type model for temperature, which is extended in this article to address the multi-zone modelling case. Experimental results are presented for a laboratory forced ventilation chamber, instrumented with 30 thermocouples, and recommendations are given for future application to a closed--environment agricultural grow cell being developed by the authors and industrial partners.

Keywords: Sampled data control, Linear systems, Optimal control
Abstract: This paper provides a method for the L_1 analysis of sampled-data systems, by which we mean the computation of their L_infty-induced norm. We first apply the lifting approach to sampled-data systems and derive an operator theoretic representation of their inputslash output relation. We then apply fast-lifting by which the sampling interval [0,h) is divided into M subintervals with an equal width, and provide methods for computing the L_infty-induced norm. Specifically, we use an idea of kernel approximation approach, in which the kernel function of an input operator and the hold function of an output operator are approximated by staircase or piecewise linear functions. Furthermore, it is shown that the approximation errors in staircase or piecewise linear approximation are ensured to be reciprocally proportional to M or M^2, respectively.

Keywords: Sampled data control, Stability of nonlinear systems, Delay systems
Abstract: This paper addresses the stability analysis of nonlinear rational sampled-data control systems with zero-order-hold over communication networks. It is assumed that the sampling interval may be time-varying (to deal with aperiodic sampling) and the communication network is modeled by an induced varying time-delay. In this setup, considering a differential-algebraic representation framework of rational systems and an input time-delay approach, Lyapunov-Krasovskii based conditions to ensure the asymptotic stability in ellipsoidal regions are derived. Based on these conditions, convex optimization problems with linear matrix inequalities constraints are proposed to either determine an estimate of the region of attraction of the system zero equilibrium point, or maximize an upper bound on the largest admissible network induced delay or on the maximal sampling interval for which the asymptotic stability of the closed-loop system is guaranteed with respect to a given set of admissible initial conditions.

Keywords: Linear systems, Sampled data control, Signal processing
Abstract: In this paper we present a right inversion scheme based on the essential concept of reachability. This scheme inverts a Hurwitz stable system one step ahead. We illustrate our procedure with the simulation of an ideal inverted pendulum.

Keywords: Stability of hybrid systems, Adaptive systems, Switched systems
Abstract: In this paper, a new algorithm is proposed for the design of a family of controllers to be used within an adaptive switching control scheme. The resulting switching controller is able to attenuate the effects of disturbances having uncertain and possibly time-varying characteristics, as well as to ensure stability under arbitrary switching sequences. Specifically, the stability requirement is addressed within the synthesis of the set of controllers by imposing some constraints in LMI form. The overall synthesis algorithm is formulated in terms of convex optimization problems, which can be solved by means of standard tools. The validity of the proposed solution is underlined by showing simulation results on an adaptive optics case study.

Keywords: Switched systems, Optimal control, Optimization
Abstract: This paper demonstrates, how an approximation of the costate trajectory can be obtained for switched systems with state jumps, when an optimal control problem with fixed switching sequence is solved using a direct method, i.e. direct shooting or collocation. The obtained trajectories include the jump conditions for the costate given by necessary conditions for optimal control of switched systems.

Keywords: Switched systems, Sampled data control, Power electronics
Abstract: This report is concerned with discrete-time systems that are derived for continuous-time LTI systems by the pulse-width-modulation (PWM) -hold. The input term of the difference equation describing the discrete-time system is a nonlinear map of the control parameter of the PWM signal, i.e., duty ratio. It is shown that for two-dimensional systems, the nonlinearity of the PWM-hold systems can be exactly ompensated by varying the center of each rectangular pulse-waves as well as its duty ratio.

Keywords: Switched systems, Stochastic systems, Discrete event systems
Abstract: This paper addressed the stability, as well as an upper bound on the lgain of linear switched state-multiplicative stochastic systems. The switching law is assumed to obey a dwell time constraint. The results are achieved by assigning each subsystem its own Lyapunov function. The Lyapunov function is time varying during the dwell time and becomes time invariant afterwards. The Lyapunov function is required to be non-increasing at the switching instances. If the dwell time approaches zero - the standard quadratic conditions are recovered. Stability and performance are guaranteed in the mean-square sense by requiring the expected value of the Lyapunov function to decrease, both for nominal systems and systems that entail polytopic-type parameter uncertainties. The theory is then extended to state-feedback controller design. The conditions are all given in terms of linear matrix inequalities.

Keywords: Switched systems, Adaptive control, UAV's
Abstract: This paper presents a sigmoid based variable coefficient PID (SBVC-PID) controller design for Twin Rotor MIMO System (TRMS). The proposed SBVC-PID controller dynamically changes controller coefficients according to a modified sigmoid function of the error signal. The modified sigmoid function is used to limit variability of PID controller coefficients in a predefined range. In the proposed method, each parameters of PID, namely kp, ki and kd, alter between predefined upper and lower bounds. A modified sigmoid function adjusted by a transition coefficient is used to alter each of the PID parameters between these bound limits. The variable coefficients of SBVC-PID maintain a hypercube in kp, ki and kd parameter space satisfying robust stability of the system. Well-known Kharitonov polynomials are used to ensure that the SBVC-PID coefficient alteration takes place in the robust stability intervals. Due to dynamically change of PID coefficients depending on magnitude of error signal, the control performance can be improved compared to conventional PID control. Performance of SBVC-PID controller is demonstrated via theoretical examples and TRMS rotor control simulations.

Keywords: Petri nets, Discrete event systems
Abstract: The aim of behavioural identification of Discrete Event Systems is to build, from a sequence of observed inputs/outputs events, a model that exhibits both the direct relations between inputs and outputs events (i.e. the reactive or observable behaviour of the system) and the internal state evolutions (i.e. the unobservable behaviour). Once the observable behaviour has been modelled by an Interpreted Petri Net, the method proposed in this paper aims at discovering the unobservable part from a firing sequence of previously discovered observable transitions. The principle is to project the firing sequence on subalphabets to discover specific patterns that are characteristic of dependancy relationships between the transitions. These relationships can be translated into Petri Net structure fragments that will be assembled to form the final model. A parametric algorithm is proposed to conduct the discovery, the choice of the minimal degree of places as a parameter being motivated by the reduction of the search space and the fitness of the final model.

Keywords: Switched systems, Stochastic systems, Identification for hybrid systems
Abstract: In this paper, we study a class of stochastic hybrid systems with piecewise linear partitioned state space, and state-depending switching governed by an intensity function. Using maximum likelihood methods, we develop a method for estimating parameters of switching distributions in such systems. This is accomplished by identifying the trajectories of a stochastic hybrid system with a point process. The efficiency of the findings are demonstrated on an example.

Keywords: Signal processing, Stability of nonlinear systems, Adaptive systems
Abstract: This paper introduces a novel deadbeat frequency estimator for possibly biased noisy sinusoidal signals. The proposed estimation scheme is based on processing the mea- surements by Volterra integral operators with suitably designed kernels, that allow to obtain auxiliary signals not affected by the unknown initial conditions. These auxiliary signals are exploited to adapt the frequency estimate with a variable structure adaptation law that yields finite-time convergence of the estimation error. The worst case behavior of the proposed algorithm in the presence of bounded additive disturbances is characterized by Input-to-State Stability arguments. Numerical simulations are given to show the effectiveness of the proposed method and to compare it with some other techniques available in the recent literature.

Keywords: Robust control, Identification for control, H2/H-infinity methods
Abstract: This paper reports an improvement in the control design procedure of iterative identification and control design for partially unknown unstable (not necessarily minimum-phase) systems. It proposes a systematic two-step control design approach, which ultimately results in a two degrees-of-freedom structure. In this approach, the unstable plant is first stabilized by a parallel feedback stabilizer with minimum weighted energy. In the second step of the design, a mixed-sensitivity H_∞ controller is designed on the basis of the stabilized plant to improve the overall performance of the closed-loop system. Through the proposed method, the bandwidth of the overall closed-loop system can be systematically expanded (increased) in the second step of the design. The effectiveness of this algorithm is verified by a numerical example and a real-time experiment on a non-minimum phase unstable active magnetic bearing system. The proposed method offers a simple but effective design structure which provides desirable results that may not be achievable by a single-step controller design method.

Keywords: Signal processing, Differential algebraic systems
Abstract: This paper extends the application of the unscented Rauch-Tung-Striebel smoother to nonlinear descriptor systems, where the mean and covariance estimates of the algebraic states can also be computed. The consistency in the smoother solution is ensured through the unscented transformation of the differential state estimates. The method also allows for measurements that are functions of both differential and algebraic states. The performance of the proposed smoother is demonstrated by an electrochemical case study.

Keywords: Distributed parameter systems, Lyapunov methods
Abstract: We consider the problems of trajectory generation and tracking for general 2 times 2 systems of first-order linear hyperbolic PDEs with anti-collocated boundary input and output. We solve the trajectory generation problem via backstepping. The reference input, which generates the desired output, incorporates integral operators acting on advanced and delayed versions of the reference output with kernels which were derived by Vazquez, Krstic, and Coron for the backstepping stabilization of 2times 2 linear hyperbolic systems. For tracking the desired trajectory we employ a PI control law on the tracking error of the output. We prove exponential stability of the closed-loop system, under the proposed PI control law, when the parameters of the plant and the controller satisfy certain conditions, by constructing a novel "non-diagonal" Lyapunov functional.

Keywords: Distributed parameter systems
Abstract: The paper is concerned with an alternative method in addressing the effects of spatiotemporally varying disturbances in controlling spatially distributed systems. Use of robust control schemes for controlling partial differential equations may not provide acceptable controller authority in handling ``moving'' disturbances. A way to handle such a case is to consider the use of mobile actuators. In this work, we consider a class of spatially distributed systems which employ a collocated actuator/sensor pair. By using the a priori defined structure of static output feedback, the problem then remains that of determining the spatial repositioning of the actuatro/sensor pair throughout the spatial domain. Using energy-based methods based on the state norm of the spatially distributed system, two guidance policies associated with two different actuator distribution functions are developed. Simulation results for a 1D diffusion equation with a ``moving'' disturbance are included to provide some insight on the effective handling of such moving disturbances via mobile actuator/sensor pairs.

Keywords: Nonlinear system theory, Distributed parameter systems
Abstract: Many natural phenomena and engineering applications are based on synchronization between several periodic processes. A commonly known example is a phase-locked loop (PLL), that is, a feedback circuit providing synchronization between the endogenous oscillator and exogenous periodic signal in phase. Imprecise recovery of the signal’s phase leads to decoding and demodulation errors, so the properly designed PLL must provide the fast “phase-locking”, i.e. convergence of the phase shift (or error) to a steady value. In the simplest situation the error converges to the nearest equilibrium; in general, due to the initial conditions or disturbances, it can leave this basin of attraction and converge to another equilibrium. During this undesirable transient process, referred to as the cycle slipping, the phase shift is increased by a multiple of the period. The mechanical analog of a slipping PLL is a pendulum, making several turns around the point of suspension before stabilization at the lower equilibrium. In this paper we estimate the number of slipped cycles for a class of synchronization systems, governed by integro-differential Volterra equation with a scalar periodic nonlinearity and including, particularly, PLLs with discrete or distributed delays in the loop. These estimates are extended to singularly perturbed Volterra equations, having a small parameter at the higher derivative. Such models naturally arise if the system has “slow” and “fast” dynamics.

Keywords: Distributed parameter systems, Optimization, Optimal control
Abstract: This contribution presents the optimal control of an induction heating process. The formal Lagrangian technique is applied to the optimal control problem to derive the first-order optimality conditions in terms of a first optimize then discretize approach. It is shown how a gradient algorithm in combination with FEM software can be used to numerically solve the optimality conditions consisting of partial differential algebraic equations of several coupled physical domains in a straightforward manner.

Keywords: Distributed parameter systems, Automotive, Linear systems
Abstract: This work focuses on the development of a state feedback regulator for a class of first order hyperbolic PDE systems with spatially varying coefficients and single point observation. The plant is assumed to be exponentially stabilizable and driven by a linear finite dimensional exosystem which is neutral stable and generates the reference signal and disturbance for the plant. The regulator design problem is to control the fixed plant such that the plant output tracks the reference signal and/or rejects the disturbance. Under the standard assumption of stabilizability, this work shows that the solvability of a constrained Sylvester equation is sufficient to guarantee the solvability of the regulator problem. Moreover, the Riccati and Lyapunov equations are utilized to provide a choice of stabilizing feedback gain which guarantees the closedloop stability. An adequate numerical example of constant tracking for the first order hyperbolic PDE system with spatially varying coefficients is explored within the proposed regulator design.

Keywords: Predictive control for linear systems, Linear systems, Observers for linear systems
Abstract: Offset-free Model Predictive Control formulations refer to a class of algorithms that are able to achieve output tracking of reference signals despite the presence of plant/model mismatch or unmeasured nonzero mean disturbances. The general approach is to augment the nominal system with disturbances, i.e. to build a disturbance model, and to estimate the state and disturbance from output measurements. Some alternatives are available, which are based on a non augmented system with state disturbance observer, or on velocity form representations of the system to be controlled. In this paper, we review the disturbance model approach and two different approaches in a coherent framework. Then, differently from what is reported in the literature, we show that the two alternative formulations are indeed particular cases of the general disturbance model approach.

Keywords: Predictive control for linear systems, Large-scale systems, Emerging control theory
Abstract: This paper deals with the control of systems for which there is a clear distinction between preferred and auxiliary actuators, the latter to be used only when the control error is large. Explicit MPC and exact penalty functions are used to show how LASSO-MPC can implement this idea. Two LASSO- MPC versions are reviewed, that allow the designer to impose a certain nominal operations zone, namely, a neighbourhood of the set-point in which the auxiliary actuators are never used. For the sake of brevity, the required procedures are shown only for version 1, but it is also discussed how they can be extended to version 2. Limitations due to the presence of constraints are also formalised. The LASSO-MPC version 1 can be used to embed an existing linear quadratic MPC, while LASSO-MPC version 2 can be used to obtain multiple levels of priority. The paradigm is demonstrated for version 1 through the control of the linearised lateral dynamics of a Boeing 747. In particular, the approach uses the spoilers only when the control error is larger than a desired threshold.

Keywords: Predictive control for linear systems, Predictive control for nonlinear systems, Optimal control
Abstract: Economic model predictive control (eMPC), where an economic objective is used directly as the objective function of the control system, has gained much popularity in recent literature. However, with a purely economic objective, the control designer has no influence over the control performance of the process. In this paper, we propose a means of tuning the objective function in order to give some level of control performance. Also, the stability proof for eMPC relies on some strict-dissipativity condition. We also show how this condition can be satisfied when the system is only dissipative with respect to the original objective function.

Keywords: Predictive control for linear systems, Process control, Chemical process control
Abstract: Since the beginnings in the chemical and process industry, model based predictive control strategies have become widely accepted. Often mentioned success factors for MPC are the use of optimization based on a plant model, the consideration of constraints, and an intuitive tuning. Indeed, if a nominal plant and overall objective are known, the tuning can become straightforward. However, as soon as disturbances have to be taken into account, the tuning effort increases and becomes less intuitive. Against this background, a novel strategy to address the issues with unknown disturbances is proposed. The idea is to separate the nominal tuning process and extend the control by an outer loop, which ensures offset-free control. The inner, nominal loop decouples the system and essentially leads to a first order response. This inner loop addresses the performance targets in the nominal case, and the outer loop provides offset-free control in case of unknown disturbances. The outer loop consists of feedback controllers adapting the reference, which due to the decoupling can be tuned by known guidelines. The proposed strategy is presented and evaluated using a simulated case study.

Keywords: Predictive control for linear systems, Stability of linear systems, Identification for control
Abstract: In this paper, the thermo-acoustic coupling between a laminar pre-mixed flame and an existing Helmholtz mode in a combustion chamber in various operating points (OPs) is studied experimentally. A parametric reduced order model is employed to represent the system in both stable and unstable OPs and the corresponding values of the model parameters in each OP are obtained. The model is then used in a Model Predictive Controler (MPC) for predicting the future behavior of the system. The Pade approximation of the phase shifter is transformed to its equivalent state feedback regulator, which can stabilize the real system, although in a limited range of OPs. Then, by proposing a novel Closed-Loop Paradigm which uses this regulator as an internal stabilizer of a dual-mode MPC, we improved the controler performance in a wider range of OPs.

Keywords: Network analysis and control, Nonlinear system theory
Abstract: In this paper we present new results on asymptotic consensus for continuous-time nonlinear time varying networks. A key feature in the following is that the monotonicity property (i.e. cooperativity) is not required, unlike most of existing literature on the subject. Additionally, we extend the use of a "State Frozen" concept [Manfredi-Angeli13] and integral connectivity to this non-trivial scenario, and give condition for consensus with the additional merit to be frozen in state variables and therefore of simpler verification. Finally, we give an estimate of the exponential rate of convergence towards the agreement manifold.

Keywords: Network analysis and control, Distributed control, Concensus control and estimation
Abstract: We derive sufficient conditions on the eigenvectors and eigenvalues of a matrix for letting it be the Laplacian of an undirected, weighted graph. The derived conditions are convex conic and apply to network synthesis problems. We present an algorithmic implementation of the proposed synthesis procedure.

Keywords: Network analysis and control, Optimization, Game theoretical methods
Abstract: We consider a routing game played on a graph, in which different populations of drivers (or packet routers) iteratively make routing decisions and seek to minimize their delays. The Nash equilibria of the game are known to be the minimizers of a convex potential function, over the product of simplexes which represent the strategy spaces of the populations. We consider a class of population dynamics which only uses local loss information, and which can be interpreted as a mirror descent on the convex potential. We show that for vanishing, non-summable learning rates, mirror descent dynamics are guaranteed to converge to the set of Nash equilibria, and derive convergence rates as a function of the learning rate sequences of each population, and illustrate these results on numerical examples.

Keywords: Network analysis and control, Control over networks, Optimization
Abstract: We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show that network coherence is a submodular function of the network topology. As a consequence, a simple greedy algorithm is guaranteed to produce near optimal edge set selections. We also show that fast rank one updates of the Laplacian pseudoinverse using generalizations of the Sherman-Morrison formula and an accelerated variant of the greedy algorithm can speed up the algorithm by several orders of magnitude in practice. These allow our algorithms to scale to network sizes far beyond those that can be handled by convex relaxation heuristics.

Keywords: Network analysis and control, Stability of nonlinear systems, Concensus control and estimation
Abstract: Whereas synchronization (consensus, agreement) in linear networks has been thoroughly studied in recent years up to certain exhaustiveness, reaching a synchrony among general nonlinear agents still remains a hard open problems. In this paper, we propose a general criteria of synchronization in undirected networks with nonlinear nodes, based on the idea of incremental dissipativity. We show that our result implies a number of existing synchronization criteria, employing incremental Lyapunov functions (such as e.g. the sum of squared deviations between the agents' states). At the same time, unlike most of existing results of synchronization, our criterion is applicable not only to linearly coupling maps, but also to a wide class of nonlinear couplings, provided they are anti-symmetric and satisfy a quadratic constraint, which should be in correspondence with the incremental supply rate and the network topology. Our criterion thus allows to extend many existing synchronization criteria to the case of nonlinear couplings; moreover, it can be applied to some classes of agent, uncovered by previous results, among them are nonlinear agents in Lurie form and biochemical oscillators of Goodwin's type.

Keywords: Stability of nonlinear systems, Feedback linearization, Variational methods
Abstract: A contraction based stabilization problem of systems with approximate strict feedback form is considered here. A high gain feedback is used to force the system into singularly perturbed form. Contraction theory based recursive controller design and singular perturbation analysis is used to design a stabilizing controller for the whole system. It is shown that, explicit error bounds between trajectories of fast subsystem and the slow manifold remain within the desirable limits by proper choice of controller parameters. Contraction theory based controller design and analysis has been expanded to a new class of systems.

Keywords: Optimal control, Constrained control, Nonlinear system theory
Abstract: The paper aims to develop the framework for optimal nonlinear model predictive controller (NMPC) with guaranteed uniform asymptotic stability for nonlinear systems with bounded perturbations. More specifically, the solution to the problem of optimal control for state constrained dynamics with bounded input is characterized and the concepts that provide the tools to determine the value function and the optimal control feedback are presented. Under mild assumptions we require that NMPC keeps the state inside some limits of interest and we provide explicit bounds of the evolution for the closedloop system state and its correlation with control law. The main idea is to design Lyapunov-based predictive controller which would allow the local control law, in the presence of bounded perturbation, to maintain the deviated trajectory inside the tolerable limits. It is shown that the properly defined controller can significantly improve the response by making the use of strict state constraints. The optimal input is computed based on constrained optimal algorithms.

Keywords: Nonlinear system theory, Constrained control, Optimal control
Abstract: Many authors dealt with several questions concerning the control of parabolic PDEs. The study of null controllability of systems of partial differential equations, which are essentially met in physics, chemistry or in biology, continues to interest nowadays, and numerous articles are dedicated to it in the literature. In chemistry or in biology, those systems can model the evolution in time of a chemical concentration or a density of population (of bacteria, cells).

We propose a new contribution in the domain of null controllability of parabolic system with nonlocal operator. Our topic is concerned with the control of a cascade system of non-linear coupled equations, with a constraint imposed to the control. The proof of the existence of a control satisfying the null controllability problem is made by proving the existence and the uniqueness of a control of minimal norm for the linear problem, associated to the studied problem. And to do that, we use in particular Carleman inequalities that we state for a nonlocal operator. Thus we build a map and we apply the Schauder fixed point Theorem to show that the map admits a fixed point.

Keywords: Nonlinear system theory, Differential algebraic systems, Delay systems
Abstract: In this paper for the class of nonlinear uncertain discrete time singular systems with time delay we present robust stability analyze results. Next, we consider a control problem for nonlinear uncertain discrete time singular systems with time delay involving a notion of optimality with respect to an auxiliary cost which guarantees a bound on the worst-case value of a nonlinear nonquadratic cost criterion over a prescribed uncertainty set. Further we specialize result to affine uncertain discrete time singular systems with time delay to obtain controllers predicated on an inverse optimal control problem. In particular, to avoid the complexity in solving the steady-state Hamilton-Jacobi-Bellman equation we parameterize a family of stabilizing controllers that minimize some derived cost functional that provides flexibility in specifying the control law. The performance integrand is shown to explicitly depend on the nonlinear singular system with time delay dynamics, the Lyapunov function of the closed-loop system, and the stabilizing feedback control law wherein the coupling is introduced via the Hamilton-Jacobi-Bellman equation. By varying the parameters in the Lyapunov function and the performance integrand, the proposed framework can be used to characterize a class of globally stabilizing controllers that can meet the closed loop system response constraints. Obtained results for nonlinear case are further specialized to linear discrete time singular systems with time delay case.

Keywords: Nonlinear system identification, Identification, Uncertain systems
Abstract: A contraction based identification scheme for systems with nonlinear parameterizations is developed in this paper. Given a system with a general parameterization, an identification model is proposed such that the time evolution of estimation error is composed by two blocks of parameterization: one linear and one nonlinear function of linear parameterization. A particular identification algorithm, based on the proportional-integral adaptive scheme, is then formulated. Stability and parametric convergence are analyzed in terms of exponential convergence among the underlined and desired identification systems trajectories by means of an averaged version for contraction.

Keywords: Agents networks, LMI's/BMI's/SOS's, Linear systems
Abstract: This paper deals with the consensus problem of linear systems from an integral perspective considering the dynamics of the agents and graph theoretical descriptions of the network. A consensus algorithm is defined as the interaction of two properties inherent to a network: hierarchical organization and information exchange. From this definition the problem is tackled as the stability of some coordination variables by means of Lyapunov functions and LMI methodology. This approach allows to define precision and speed indicators to evaluate the performance of different algorithms related to the agents' dynamics. The main characteristics of this approach are discussed with the help of the consensus canonical example of double integrator systems and complemented with an analysis and design example.

Keywords: Agents networks, Network analysis and control, Control over networks
Abstract: A network of discrete-time agents (nodes) which can be controlled by different nodes, acting independently, is considered. When a network can be controlled through several nodes, it is important to understand differences in choosing a particular node as driver node (node which control the entire network). This work considers limited actuator amplitude of driver node and characterizes driver node based on Region of Attraction (ROA) obtained corresponding to a particular chosen driver node. The presented theory and algorithms enable to find an appropriate node such that Region of Attraction maximizes. Theoretical developments are verified through numerical simulation.

Keywords: Agents networks, Optimal control, Randomized algorithms
Abstract: This paper deals with a "differentiated consensuses" problem in a distributed stochastic network system with priorities. The network is considered as a set of heterogeneous agents that process incoming tasks with different importance (priority) levels. The observations about neighbors’ states are supposed to be obtained with random noise and delays and the topology could switch over time. Several consensus objectives are to be achieved. To maintain almost balanced load, i.e. approximate consensus for every priority class across the network, a new family of control protocols that use different step-size parameters for each task class is introduced. An instrument for choosing optimal step-sizes for the proposed control strategy is given. In addition, a numerical example that illustrates the proposed control strategy and the results of simulations are provided.

Keywords: Agents networks, Optimization algorithms, Concensus control and estimation
Abstract: This paper deals with a distributed constraint optimization problem on networked multi-agent systems. First, we propose a complete distributed algorithm based on the Lagrangian method which does not rely on supervisors. A new method to estimate the Lagrangian multiplier is proposed which enables each agent to obtain the Lagrangian multiplier in a distributed manner. Next, we derive a necessary and sufficient condition that the optimization problem is solvable in a distributed manner over a given network. Finally, a numerical example illustrates the effectiveness of the proposed method.

Keywords: Distributed estimation over sensor nets, Agents networks, Cooperative autonomous systems
Abstract: We propose a distributed regression algorithm with the capability of automatically calibrating its parameters during its on-line functioning. The estimation procedure corresponds to a Regularization Network, i.e., the structural form of the estimator is a linear combination of basis functions which coefficients are computed by solving a linear system. The automatic tuning strategy instead constructs and then exploits opportune bounds on the distance between the distributed estimation results and the unknown centralized optimal estimate that would be computed processing the whole dataset at once. By numerical simulations we show how the proposed procedure allows the sensor networks to effectively self-tune the parameters of the distributed regression scheme by simple consensus strategies.

Keywords: Energy systems, Electrical power systems, Game theoretical methods
Abstract: The main objective of this paper is to design electric vehicle (EV) charging policies which minimize the impact of charging on the electricity distribution network (DN). More precisely, the considered cost function results from a linear combination of two parts: a cost with memory and a memoryless cost. In this paper, the first component is identified to be the transformer ageing while the second one corresponds to distribution Joule losses. First, we formulate the problem as a non-trivial discrete-time optimal control problem with finite time horizon. It is non-trivial because of the presence of saturation constraints and a non-quadratic cost. It turns out that the system state, which is the transformer hot-spot (HS) temperature here, can be expressed as a function of the sequence of control variables; the cost function is then seen to be convex in the control for typical values for the model parameters. The problem of interest thus becomes a standard optimization problem. While the corresponding problem can be solved by using available numerical routines, three distributed charging policies are provided. The motivation is threefold: to decrease the computational complexity; to model the important scenario where the charging profile is chosen by the EV itself; to circumvent the allocation problem which arises with the proposed formulation. Remarkably, the performance loss induced by decentralization is verified to be small through simulations. Numerical results show the importance of the choice of the charging policies. For instance, the gain in terms of transformer lifetime can be very significant when implementing advanced charging policies instead of plug-and-charge policies. The impact of the accuracy of the non-EV demand forecasting is equally assessed.

Keywords: LMI's/BMI's/SOS's, Power electronics, Lyapunov methods
Abstract: In this paper, stabilization of a class of power converters with discrete-time bilinear averaged dynamic model is investigated by using Sum of Squares (SOS) programming and quadratic Lyapunov functions. A general bilinear mathematical discrete model is derived for a class of DC/DC power converters and the coordinates of the developed model are transformed to the origin. A controller design methodology based on SOS programming that has been developed in previous works is applied to various power converter models. The controller design allows for maximizing the region of convergence, and/or guaranteeing a certain exponential rate of decay, while input constraints are fulfilled. The resulting controller designs are evaluated using detailed switching models, and are shown to compare favorably with controller designs available in literature.

Keywords: Electrical machine control, Automotive, Optimal control
Abstract: This paper introduces a novel set of electric motor degradation cost functions based on energy usage, energy loss and work output, against their continuous operation rated values recommended by the manufacturer. Unlike conventional electric motor degradation indicators such as the bearing life and insulation life based service factors, these cost functions account for the quantified time in the degradation process. The cost functions are evaluated throughout the operational life of the motor using real-time measurements. Hence, they give a very accurate indication, which may be adapted for online controller tuning. This solid establishment of a degradation cost function also enables the system designer to give the user a choice between performance and degradation minimization. The proposed cost function scheme has experimentally been verified using a hardware-in-the-loop electric powertrain testrig where standard drive cycles are used to conduct the experiments. The experimental results reveal that the degradation cost functions Cumulative Input Energy Ratio (CIER), Cumulative Loss Ratio (CLR) and Cumulative Work Ratio (CWR) accurately represent the electric motor degradation both qualitatively and quantitatively.

Keywords: Electrical machine control, Fuzzy systems, Robust adaptive control
Abstract: We propose in this paper an adaptive robust fuzzy observer to estimate flux and to identify the load torque for Induction Machine’s (IM) applications. Indeed, using a fuzzy IM model, we develop the structure of an observer where we consider the load torque as an unknown input. Sufficient conditions are presented to ensure the asymptotic convergence of the flux and the load torque errors estimation. In addition, a robustness criteria is considered, using the L2 technique, to take into consideration parameters uncertainties. Design conditions are founded on LMIs terms (Linear Matrix Inequalities) and an experimentation (using DSP 1104 real time controller) is carried out to show the effectiveness of the proposed results.

Keywords: Electrical machine control, Servo control, Fuzzy systems
Abstract: Tuning a PI controller can be quite cumbersome for the non-expert as the closed-loop control system has to meet various requirements while the influence and interaction of the two degrees of freedom are not always clear. This paper addresses the design of an iterative PI controller autotuning for drive systems with the idea of imitating a human expert. In contrast to existing concepts, a new approach with multiple tuning strategies is applied which gives a compact rule base that is easy to modify. The performance of the proposed algorithm is illustrated through motion control testbench trials.

Keywords: Output regulation
Abstract: This paper deals with the problem of synthesizing feedforward control to aid the regulation of web tension in the presence of partially known exogenous inputs. The problem appears in many engineering applications including Roll-to-Roll (R2R) manufacturing systems where the governing equation for tension is nonlinear. Currently known methods for the nonlinear output regulation problem either require the solution of a constrained partial differential equation or the preview information of the signal to be tracked. In this paper, we consider the problem of regulating web tension while rejecting periodic disturbances and use a novel approach to synthesize feedforward control as the solution of a system of differential-algebraic equations, which is considerably less complex and suitable for practical implementation. We assume that the disturbance signal is the output of a known exogenous system with unknown initial conditions. A parameter identification scheme to estimate the unknown initial conditions is developed. The proposed technique is successfully applied to web tension regulation in a large R2R machine which contains real-time hardware and software that is used in industrial practice. Extensive experiments were conducted to evaluate the proposed scheme under various experimental conditions, including different web speeds and materials. We will discuss a representative sample of the results with the proposed nonlinear tension regulator and provide a comparison with a well-tuned industrial PI control scheme to highlight the benefits of using the proposed scheme.

Keywords: Robust control, Manufacturing processes, Modeling
Abstract: The parameter space approach method for stability chart calculation is a well-known method. There are various analysis and fine-tuning tools available for controller design which are based on the determined stabilizing controller parameter space. Unfortunately the parameter space approach is currently only systematically developed and implemented for single loop PID controller tuning. This work presents an easy way (based on decoupling techniques) to expand the synthesis step of the classical parameter space approach to MIMO systems (with multiple time delay). The developed method is illustrated on the application example of a vacuum thermal evaporation process (VTA). Regarding this example, the presented approach is used to tune the parameters of the internal PID heat controllers. The VTA-process is characterized in detail before the controller design starts. Furthermore a physical model which describes the heat transfer in the process is obtained.

Keywords: Sliding mode control, Mechatronics, Uncertain systems
Abstract: In this paper, a quasi-continuous sliding mode control is applied for the tracking control of a hydrostatic transmission. The nonlinear dynamic model of the considered system consists of four first-order differential equations characterised by both parametric uncertainty due to uncertain physical parameters and unknown disturbances, the leakage volume flow as well as a resulting load torque. A nonlinear reducedorder state and disturbance observer is employed to estimate the unmeasurable system states and disturbances online. The proposed control structure is validated both by simulations and experiments. A comparison with flatness-based control shows that a superior tracking accuracy can be achieved for the normalised motor bent axis angle and the motor angular velocity as controlled variables.

Keywords: Transportation systems, Modeling
Abstract: This paper addresses the problem of designing a speed limiter for an electrically assisted kick scooter. A control-oriented model of the longitudinal dynamics is first derived, by taking into account the scooter/human interaction. A coasting-down experiment is then carried out for parametric identification. Two different speed limiting architectures are finally studied and experimentally tested: a relay-based scheme and a torque controller with dynamical saturation.

Keywords: Iterative learning control, Mechatronics
Abstract: The present paper proposes an iterative learning control (ILC) algorithm for accurate force tracking in a long range tribometer. The device is a nonlinear single input single output plant affected by repetitive and non repetitive perturbations in the output. The former perturbations result from the repetitive nature of the tests, and the latter ones are caused by friction phenomena in the guiding elements. Due to the characteristics of the device, it has been necessary to develop specific solutions to assure a robust behavior: on the one hand, analysis and identification techniques for the perturbations, and on the other hand, a spatial synchronization. The finally developed controller combines ILC with feedforward and feedback commands. The system is experimentally validated and the results show a substantial improvement in the performance compared to more classical approaches.

Keywords: Output feedback, Optimization algorithms, Intelligent systems
Abstract: The problem we research is to construct such control function that autonomously provides control commands upon the received values of the object’s state. We formulated mathematically the problem of control synthesis. The goal of synthesis is to find a multidimensional control function that depends on the current states of all objects. The synthesized control function adjusts any time the optimal control values to allow each robot achieving the objectives with the best quality functional value. The network operator method is used to solve the problem. The effectiveness of the proposed method is demonstrated in simulations on a team of two mobile robots performing a parking task.

Keywords: Optimization algorithms, Distributed cooperative control over networks, Concensus control and estimation
Abstract: Multi-agent optimization problems arise in a wide variety of networked systems, and are often required to be solved in an asynchronous and uncoordinated way. However, existing asynchronous algorithms for constrained multi-agent optimization do not have guaranteed convergence rates and, thus, lack performance guarantees in on-line applications. This paper addresses this shortcoming by developing randomized coordinate descent algorithms for solving the dual of a class of constrained multi-agent optimization problems. We show that the algorithms can be implemented asynchronously and distributively in multi-agent networks. Moreover, without relying on the standard assumption of boundedness of the dual optimal set, the proposed dual coordinate descent algorithms achieve sublinear convergence rates of both its primal and dual iterates in expectation. The competitive performance is demonstrated numerically on a constrained optimal rendezvous problem.

Keywords: Optimal control, Stochastic control, Optimization
Abstract: We consider the problem of minimizing the long-run expected average cost of a complex system consisting of interactive subsystems with an emphasis on advanced propulsion systems, e.g., hybrid electric vehicles. We formulate a multiobjective optimization problem of the one-stage expected costs of the subsystems and provide a framework to prove that the control policy yielding the Pareto optimal solution minimizes the average cost criterion of the system.

Keywords: Optimization algorithms, Signal processing, Computational methods
Abstract: The rational covariance extension problem is to parametrize the family of rational spectra of bounded degree that matches a given set of covariances. This article treats a circulant version of this problem, where the underlying process is periodic and we seek a spectrum that also matches a set of given cepstral coefficients. The interest in the circulant problem stems partly from the fact that this problem is a natural approximation of the non-periodic problem, but is also a tool in itself for analysing periodic processes. We develop a fast Newton algorithm for computing the solution utilizing the structure of the Hessian. This is done by extending a current algorithm for Toeplitz-plus-Hankel systems to the block-Toeplitz-plus-block-Hankel case. We use this algorithm to reduce the computational complexity of the Newton search from O(n^3) to O(n^2), where n corresponds to the number of covariances and cepstral coefficients.

Keywords: Robotics, H2/H-infinity methods, Linear parameter-varying systems
Abstract: Soft Robotics and Variable Stiffness Actuation (VSA) are active research domain in robotics. The aim is to design human-friendly machines that can perform safely dexterous tasks close to or in contact with humans. Whereas most of current works focus on biomimetic VSA by using two antagonistic motors to simultaneously deal with motion control and stiffness adaptation, in this work, we present a control system approach that takes advantage of the mechanical reversibility of series elastic actuators and the recent availability of structured H-infinity synthesis. The paper introduces a methodology for the design of a control law that allows to turn a force-sensorless actuator that includes a flexible link into a variable stiffness actuator where the stiffness can be set arbitrarily in some interval. With the proposed framework, it has been possible to accurately control the motion and the stiffness of a cable-screw actuator.

Keywords: Robotics, Maritime, Optimization
Abstract: This paper addresses a control allocation method in order to compensate for the effect of thrusters’ dead-zones, on the actuation system of an underwater vehicle. This solution concurrently considers dead-zone effect and actuation limitation, in order to increase system reactivity. Experimental results are given to demonstrate the effectiveness and correctness of the proposed method.

Keywords: Robotics, Mechatronics
Abstract: In autonomous robotic surgery, the supervision of the surgeon cannot be avoided due to the unforeseenable emergencies and complications that can take place during an operation. When necessary, the surgeon has to take over the surgical system switching it from an autonomous mode to a teleoperation mode. In this paper we propose a two-layer bilateral control architecture that ensures a safe behavior during the switch and high performance during the teleoperation. Experiments are proposed for validating the architecture proposed in the paper.

Keywords: Robotics, Modeling, Autonomous robots
Abstract: This paper studies the attitude dynamics and the control of quadruped robots using tail-like appendages during the flight phases of high speed locomotion. Inspiration and data are first obtained from cheetah’s fast galloping techniques. A two-body template is then used to simply describe the dynamics of a large body whose attitude is controlled by a rotating appendage. The equations of motion for a tail and a reaction wheel are given, while by employing cyclic coordinates, all possible reductions are performed to finally lead to the design of model-based controllers. A main contribution lies on the thorough discussion on the holonomy of the system, which only depends on the system’s geometry and the initial angular momentum. A comparison between a reaction wheel and a tail is also carried out, while basic steps and formulas are proposed for selecting the key parameters concerning the design of such systems. Finally, simulation results are presented in order to validate the methods proposed herein.

Keywords: Robotics, UAV's, Optimization
Abstract: In this paper, we present an optimization based method for path planning of a mobile robot subject to time bounded temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specification such as safety, coverage, motion sequencing etc. We use metric temporal logic (MTL) to encode the task specifications with timing constraints. We then translate the MTL formulae into mixed integer linear constraints and solve the associated optimization problem using a mixed integer linear program solver. This approach is different from the automata based methods which generate a finite abstraction of the environment and dynamics, and use an automata theoretic approach to formally generate a path that satisfies the TL specifications. We have applied our approach on several case studies in complex dynamical environments subjected to timed temporal specifications.

Keywords: Markov processes, Concensus control and estimation
Abstract: We search for the Markov chain with the optimal mixing rate where transitions are restricted to happen along a cycle of the states. We show that homogeneous, reversible chains are locally optimal for perturbations that make them inhomogeneous and non-reversible. Moreover, we show the optimality holds globally if only a single type of perturbation (either inhomogeneous or non-reversible) is applied. However, we conjecture global optimality holds for mixed perturbations as well, which is backed by simulation results. This paper complements previous results on bounds for mixing times of general Markov chains on the cycle.

Keywords: Markov processes, Model/Controller reduction
Abstract: In this paper, we study a new way to define state aggregation of inhomogeneous Markov chains. This method consists in defining simulation morphisms between inhomogeneous Markov chains using their associated spaces of zero- charge measures and the evolution semi-groups that arise from their transition matrices.

Keywords: Markov processes, Stochastic systems, Nonlinear system theory
Abstract: The note presents conditions to assure the stability in probability for a class of continuous-time quadratic Markov jump systems. From the viewpoint of the state-space evolution, the system has two parts: (i) a linear term, in which the matrix parameter jumps according to a Markov chain, and (ii) a quadratic term with no jumps. The stability in probability for the quadratic Markov jump system is then assured under mild conditions. A numerical example illustrates the usefulness of the derived results.

Keywords: Quantized systems, Stochastic systems, Control over networks
Abstract: In lots of control systems for recent applications, their components are interconnected to various information networks. In such systems, transmission data rate limitation is ubiquitous among these components. In addition, detection of malicious attack is an urgent issue. In this paper, to manage such situations, replay attack detection in control systems with quantized signals is studied. We propose a novel scheme where dithering noise plays a role of randomizing quantization error and also of a time stamp for detecting the malicious data manipulation. In order to evaluate the resulting regulation and detection ability, we extend our previous results on the stationary variance approximation in control systems with random dither quantization. The effectiveness is exhibited through numerical examples.

Keywords: Intelligent systems, Complex systems, Stochastic systems
Abstract: The main purpose of biological memory is to robustly recognize objects and concepts, not to reconstruct their copies. For this the memory should mostly record the relations among the constituents of the incoming signals, rather than the constituents themselves. Relational memories can be stored in the form of network connectivity between neurons. However, similarity testing for such spatial representations is difficult. We suggest that the spatial representations are converted to temporal representations for similarity testing, so as to enable a large scale approximate content addressable memory. This not only proposes a new way for automatic concept abstraction in data analysis, but also explains some of the mysteries in the behaviors of human and animal minds.

Keywords: Robust control, Uncertain systems, Optimal control
Abstract: The paper presents the Robust Control Toolbox for Time Delay Systems with Parametric Uncertainties for the Matlab system. The toolbox comprises the D-K iteration and the algebraic approach implemented for general 3rd order system with parametric uncertainties in numerator and denominator of plant transfer function and uncertain time delay. The uncertain time delay is treated using multiplicative uncertainty, the parametric uncertainty is modelled using general interconnection for the systems with parametric uncertainty in numerator and denominator. The toolbox has user-friendly graphical interface empowering intuitive control.

Keywords: Robust adaptive control, Electrical power systems
Abstract: The problem of disturbances compensation in multi-machine power systems under parametric uncertainties and perturbed mechanical input power is considered. The solution is proposed for the case when only relative speed of each electrical generator is available for measurement. The proposed control algorithm synchronizes the multi-machine power system with the required accuracy in the normal mode and under symmetrical 3-phase short circuit faults which occur on transmission lines. Efficiency of the proposed scheme is illustrated by modeling of the three-machine power system.

Keywords: Robust control, H2/H-infinity methods, Robotics
Abstract: The present investigation introduces a novel control strategy for hybrid dynamic systems with unilateral constraints. Sufficient conditions are presented to ensure internal asymptotic stability and external disturbances attenuation. The developed synthesis is applied to the orbital stabilization of an underactuated bipedal robot periodically touching the ground. Good performance of the closed-loop system is obtained not only in the presence of external disturbances, affecting the gait of the biped between impacts and under uncertainties at the velocity restitution when the ground collision occurs.

Keywords: Emerging control theory, Switched systems
Abstract: This paper addresses the design of a covert attack on a linear multivariable dynamical system with input hard constraints. The system evolves in the discrete-time domain and is subject to performance and alarm state constraints, both represented by convex and compact polyhedral sets. A contractive control law guarantees positive invariance of the performance set, while ensuring asymptotic stability of the origin with maximum convergence rate. An attacker succeeds in gaining control of the system and sends false control commands, when it is necessary, eventually driving the state vector outside the performance set without violating any alarm constraints. Simulation studies highlight the results of this adversary control scheme.

Keywords: Robust control, Output feedback
Abstract: Levitation controllers have become a litmus test for control algorithms. A new control algorithm that simultaneously optimizes time and frequency performance is applied to a linearized model of a levitation system. It is shown that the resulting control presents superior performances to other controls algorithms applied to the same system.

Keywords: Linear parameter-varying systems, Identification for control
Abstract: Recently, a state space identification method was developed for linear periodic parameter-varying systems in the frequency domain. The proposed algorithm required the input and scheduling signals to be periodic and synchronized. In this paper, we extend the existing approach to handle transient behavior with respect to the input. Because the system is no longer required to be in steady state, non-periodic inputs can now be used as well. We illustrate the extended identification technique on a discrete time SIMO simulation example.

Keywords: Identification for control, Process control, H2/H-infinity methods
Abstract: This paper deals with virtual reference feedback tuning (VRFT) for MIMO plants by one of the prediction based system identification (PBSID) methods. Since VRFT designs a feedback controller that minimizes the difference between the closed-loop system and the reference model, the optimized PBSID method, which minimizes the least squares of the prediction error, can be employed to estimate a full parameterization MIMO controller. Numerical examples illustrate the effectiveness of the proposed MIMO controller design methods.

Keywords: Identification for control, Automotive, Linear parameter-varying systems
Abstract: In this paper a torque-to-slip model, oriented to the development of a traction control system based on wheel slip control for powered two-wheelers, is identified. A black-box identification approach is employed to find model parameters, using I/O experimentally measured data. Different tests are employed to analyse different features of the inquired dynamics. In particular, a PRBS based identification unearths an average model; step responses are employed to study the effect of the vehicle lean angle and narrow band sine sweeps better quantify the features of an underdamped mode. The resulting model is thus a family of linear models with lean angle and velocity as scheduling parameters. The identified model is proven accurate and suitable for control system design, thanks to a closed-loop experimental validation.

Keywords: Identification for control, Robust control, Linear parameter-varying systems
Abstract: This paper discusses approximate system identification of a gas turbine operating with closed loop feedback control of the fuel and airflow. The objective is to obtain multi-input multi-output linear dynamic models to capture the system dynamics over a wide operating range of the turbine. In the proposed approximate modeling, the dynamics of a gas turbine at multiple operating conditions is described by a single multivariable model with additional scaling to account for gain variations. A covariance-based subspace system identification algorithm is applied to obtain dynamic linear models of a generalized plant model of the combined controller and gas turbine from data generated from a first principles simulation. The procedure is demonstrated to sufficiently replicate the operation of closed loop system to enable a single generalized linear model to replicate the nonlinear turbine dynamics and enable subsequent robust control design.

Keywords: Identification for control, Process control, Optimization
Abstract: Least-costly experiment design has received ample attention over the past decades, and efficient numerical algorithms that can compute optimal excitation spectra for linear models have been found. The interpretation of such spectra, however, has received far less attention. We restrict ourselves to uni-parametric models, for which an analytical solution to the experiment design problem is derived. This solution enables us to address, among other things, the following questions: What determines the frequency and amplitude of the excitation signal? Does the optimal frequency depend on the location(s) that the parameter occupies in the transfer function? With the optimal signal, is a closed-loop identification experiment cheaper than an open-loop one?

Keywords: Emerging control applications, Switched systems, Identification for control
Abstract: In this paper we apply pole placement techniques to meet the performance objectives of a web server hosted on a private cloud. The web server is modeled as a switched system with models developed for several well defined operating regions using system identification techniques. We then obtain the conditions for placement of exact and regional poles in desired locations using full state feedback to guarantee performance and stability. The experiments are performed on the open source Eucalyptus based cloud setup.

Keywords: Adaptive systems, Adaptive control, Distributed parameter systems
Abstract: This paper is focused on adaptively controlling a linear infinite-dimensional system to cause it to regulate the output to zero in the presence of persistent disturbances. The plant (A, B, C) is described by a closed, densely defined linear operator A that generates a continuous semigroup of bounded operators on a Hilbert space of states; the input-output operators B & C are finite rank linear operators . We show that there exists a direct model reference adaptive control law that regulates the output in the presence of disturbances of known waveform but unknown amplitude and phase. The conditions needed for the success of the direct adaptive controller include the need for (A, B, C) to be almost strictly dissipative (ASD). In finite dimensional space, ASD is equivalent to two simple open-loop requirements: the high frequency gain CB is sign-definite and the open-loop transfer function P(s) is minimum phase. Our main result will prove infinite-dimensional versions of these conditions for a large class of infinite-dimensional systems.

Keywords: Distributed parameter systems, Nonlinear system theory, Lyapunov methods
Abstract: This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a linear Korteweg-de Vries equation, which is a mathematical model of waves on shallow water surfaces. In this article, we close the loop with a saturating input that renders the equation nonlinear. The well-posedness is proven thanks to the nonlinear semigroup theory. The proof of the asymptotic stability of the closed-loop system uses a Lyapunov function.

Keywords: Distributed parameter systems, UAV's
Abstract: A method based on controls and computational fluid dynamics for the estimation of a gaseous plume that results from gas released into the ambient atmosphere through a moving aerial source is presented. The estimation scheme, in the form of the Luenberger observer, utilizes concentration sensor measurements provided by an unmanned aerial vehicle (UAV). The estimator is in the form of an advection-diffusion equation and is solved in real-time by a finite volume method with total variation diminishing (TVD) limiter and dynamic grid adaptation. The control algorithm for the motion of the UAV is implemented via Lyapunov redesign methods and couples the UAV dynamics to the performance of the process estimator. Numerical examples are included to illustrate the performance of the method.

Keywords: Distributed parameter systems
Abstract: This paper introduces an explicit full-state boundary feedback law that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an n-ball (which in 2-D reduces to a disk and in 3-D reduces to a sphere). The backstepping method is used to design the control law. To apply backstepping the system is reduced to an infinite sequence of 1-D systems using spherical harmonics. L² well-posedness and stability are proved. The resulting control law is written as a multiple integral whose kernel is the product of the backstepping kernel used in control of one-dimensional reaction-diffusion equations and a function closely related to the Poisson kernel in the n-ball.

Keywords: Distributed parameter systems, Process control, Adaptive control
Abstract: This paper focuses on adaptive output feedback control of transport-reaction processes described by semi-linear parabolic partial differential equations (PDEs) in the presence of unknown reaction parameters. Galerkin projection is applied to derive a low-dimensional reduced order model which employed as the basis for the adaptive controller design. The proposed control structure is a combination of a Lyapunov-based controller, an adaptation law and a static observer. The adaptation law is introduced to identify the unknown parameters while the static observer is employed to estimate the system modes required by the controller which cannot be measured directly from the process. The stability of the closed-loop system is shown using Lyapunov arguments. The effectiveness of the proposed low-dimensional adaptive output feedback control structure is illustrated on a tubular chemical reactor where the spatiotemporal dynamics of temperature and concentration are modeled by semi-linear parabolic PDEs. The control objective is considered to be thermal dynamics regulation in the presence of unknown heat of reaction.

Keywords: Distributed parameter systems, Output regulation, Robust control
Abstract: In this contribution the backstepping design of flatness-based tracking controllers for parabolic systems is extended by an integral action to acount for exogenous disturbances and model uncertainty. The proposed controller design only amounts to stabilizing an ODE by eigenvalue assignment and to applying the standard backstepping approach to a parabolic PDE. The robustness of the resulting disturbance rejection is demonstrated for model uncertainties, that do not destabilize the closed-loop system. Furthermore, it is shown, that the proposed design method allows the prevention of controller windup by a simple structural measure. The theoretical results are demonstrated by means of a parabolic system with spatially varying parameters.

Keywords: Observers for nonlinear systems, Stability of nonlinear systems, Delay systems
Abstract: Design of reduced-order observers is considered for nonlinear sampled-data strict-feedback systems with control input update delay. On the basis of the Euler-like approximate model, reduced-order observers are designed. Then the relationship between the magnitude of control input update delay and that of estimation errors is discussed. A numerical example is also given to illustrate the theory.

Keywords: Observers for nonlinear systems, Stability of nonlinear systems, Lyapunov methods
Abstract: In this paper we consider the continuous homogeneous observer defined in [Finite-time observers: application to secure communication, IEEE TAC, Perruquetti, Moulay, Floquet] in the case of the triple integrator. In [Finite-time observers: application to secure communication, IEEE TAC, Perruquetti, Moulay, Floquet], convergence of the algorithm was only proved when the degree of homogeneity was emph{sufficiently} close to 0 without more tractable information. We show here that, in the case of the triple integrator, the observer presents global finite-time stability for emph{any} negative degree under constructive conditions on the gains. This is achieved with a homogeneous Lyapunov's function design. Simulations of the proposed observer are also provided.

Keywords: Observers for nonlinear systems, Nonlinear system theory, Filtering
Abstract: The Joint Maximum Likelihood criterion is used to derive the optimal estimator for non-autonomous nonlinear dynamic systems. The solution is explicit and gives recursive formulas of the optimal estimator. The computation of the estimator's gains needs the solution of non-symmetric Differential Matrix Riccati Equation (DMRE). For linear systems this solution constitutes the structure of the Kalman Filter.

Keywords: Observers for nonlinear systems, Lyapunov methods, Algebraic/geometric methods
Abstract: This paper presents a new observer design approach for a class of discrete-time nonlinear systems described by a polytopic quasi-LPV (qLPV) models. The contribution consists in developing an observer for qLPV systems where the parameters depend on the unmeasured states of the system. The approach consists in combining the algebraic techniques with polytopic qLPV observers. Firstly, with the assumption that the nonlinear system is algebraic, or partially algebraic, observable, the unmeasured states involved in the parameters are estimated, exactly, in finite time which provides an exact estimation of the parameters. Secondly, the qLPV observer is designed by using the estimated parameters and the its finite time estimation property. Asymptotic convergence of the state estimation error is then obtained by Lyapunov analysis and LMI constraints are established, ensuring such a property and provide a way to design the gains of the observer. In addition, the transient phase is analyzed and an optimization problem under LMI constraints is provided to minimize the over-shoot of the state estimation error in the transient phase. An example is provided to illustrate the performances of the proposed approach and comparisons.

Keywords: Observers for nonlinear systems, Automotive, H2/H-infinity methods
Abstract: A robust observer is presented in this paper to estimate the longitudinal tire-road forces, the engine and braking torques for motorcycles. A study of detectability of the longitudinal dynamics is presented and the tire-road longitudinal forces are estimated using an unknown input observer without any knowledge of tire parameters. The effectiveness of the proposed approach is shown through simulation results.

Keywords: Filtering, Control over communication, Sensor and mesh networks
Abstract: We consider a remote state estimation problem, where a sensor transmits local state estimates over an independent and identically distributed (i.i.d.) packet dropping link to a remote estimator. At each discrete time instant, the sensor can decide whether to transmit or not, with each transmission incurring a fixed energy cost. Performance is quantified via an optimization problem that minimizes a convex combination of the expected error covariance at the remote estimator and expected energy usage. For transmission schedules dependent only on the error covariance at the remote estimator, this work establishes that a threshold policy (i.e. transmit if the error covariance exceeds a certain threshold and don't transmit otherwise) is optimal. This provides a rigorous justification for the use of such threshold policies in event triggered estimation. An extension of the result to Markovian packet drops is also outlined.

Keywords: Control over communication, Control over networks, Linear systems
Abstract: In this paper we consider the problem of designing coding and decoding schemes for linear control design of a scalar unstable stochastic linear system in the presence of a wireless communication channel between the sensor and the estimator. In particular, we consider a communication channel which is prone to packet loss and includes quantization noise due to its limited capacity. We first study the case of perfect channel feedback, where the transmitter is aware of the quantization noise and the packet loss history of the channel. We show that in this case, the optimal strategy among all possible linear encoders corresponds to the transmission of the Kalman filter innovation (the difference between the filtered state estimate at the transmitter and the predicted state estimate at the receiver) similarly to the differential pulse-code modulation (DPCM). Although the critical Signal-to-Quantization Noise Ratio (SQNR) required for stabilizing the system is the same for innovation forwarding as well as measurement forwarding at the transmitter, the latter is strictly suboptimal in terms of control performance. For the case of imperfect feedback, we assume that the channel feedback or acknowledgement is randomly lost with a certain erasure probability, rendering the transmitter ignorant of the control action taken by the receiver and subsequently applied to the plant. We propose several heuristic strategies for a suboptimal Kalman filter design at the transmitter based on estimation of the channel feedback status and compare their performances via numerical simulation studies.

Keywords: Control over communication, Emerging control theory, Sampled data control
Abstract: We present a novel frequency-domain analysis framework for a closed-loop model capturing a wide range of real-time and networked control systems with stochastic delays and packet drops. Our results allow for inferring the mean and variance of the output response to deterministic inputs, based on a new frequency response plot. We illustrate the usefulness of our results in the context of real-time control systems with input-to-output delays resulting from the use of a shared processor.

Keywords: Communication networks, Stochastic systems, Network analysis and control
Abstract: In this paper, we introduce a decentralized event-triggered scheduling scheme for multi-loop Networked Control Systems (NCSs) in which the individual control loops are coupled through a shared communication channel. The proposed scheduling design combines deterministic and probabilistic attributes to efficiently allocate the limited communication resource among the control loops in an event-based fashion. Based on local error thresholds, each control loop determines whether to compete for the channel access. As a result, control loops with higher transmission priorities are more likely to utilize the channel, which in turn leads to more efficient usage of the limited resource. Each eligible subsystem then attempts to transmit at times specified by local waiting times, which are randomly distributed and local-error dependent. In this manner, the probability of data collisions in the communication channel is reduced. If the channel capacity is reached at some time instants, data packets are dropped. We demonstrate stochastic stability of such NCSs in terms of Lyapunov Stability in Probability (LSP). The numerical results show that our approach improves resource utilization and reduces the networked-induced error variance in comparison with time-triggered, random access, and centralized scheduling policies.

Keywords: Cooperative autonomous systems, Concensus control and estimation, Distributed cooperative control over networks
Abstract: This paper investigates a multi-agent formation control problem with event-triggered control updates and additive disturbances. The agents communicate only by exchanging information in a cloud repository. The communication with the cloud is considered a shared and limited resource, and therefore it is used intermittently and asynchronously by the agents. The proposed approach takes advantage of having a shared asynchronous cloud support while guaranteeing a reduced number of communication. More in detail, each agent schedules its own sequence of cloud accesses in order to achieve a coordinated network goal. A control law is given with a criterion for scheduling the control updates recursively. The closed loop scheme is proven to be effective in achieving the control objective and a numerical simulation corroborates the theoretical results.

Keywords: Control over communication, Optimal control of communication networks, Control over networks
Abstract: The dimensioning of wireless communication protocols for networked control involves a non-trivial trade-off between reliability and delay. Due to the lossy nature of wireless communications, there is a risk that sensor messages will be dropped. The end-to-end reliability can be improved by retransmitting dropped messages, but this comes at the expense of additional delays. In this work, we determine the number of retransmissions that strikes the optimal balance between communication reliability and delay, in the sense that it achieves the minimal expected linear-quadratic loss of the closed-loop system. An important feature of our setup is that it accounts for the random delays and possible losses that occur when unreliable communication is combatted with retransmissions. The resulting controller dynamically switches among a set of infinite-horizon linear-quadratic regulators, and is simple to implement. Numerical simulations are carried out to highlight the trade-off between reliability and delay.

Keywords: Stability of nonlinear systems, Nonlinear system theory, Constrained control
Abstract: We consider a class of discrete-time systems with saturation previously discussed in the literature. The class may also be represented as a Lur’e system. We give a simple necessary and sufficient condition for its global asymptotic stability. The proof uses both classical multiplier theory and Lyapunov theory.

Keywords: Stability of nonlinear systems, Sampled data control, Lyapunov methods
Abstract: The paper deals with the sampled-data implementation of controllers designed by means of Immersion and Invariance stabilization techniques for a special class of dynamics. A multi-rate digital control law is derived to preserve at the sampling instants manifold attractivity. The immersion condition is guaranteed under sampling and invariance on the manifold is recovered asymptotically by the multi-rate controller, particularly well suited for the class of systems considered. The effectiveness of the proposed digital solution is shown through numerical simulations of an academic example.

Keywords: Stability of nonlinear systems
Abstract: In this paper, the discrete-time Kalman conjecture is shown to be false for systems of order two and above. Counterexamples are constructed. This contrasts with continuous-time domain systems where the Kalman conjecture is true for third-order systems.

Keywords: Stability of nonlinear systems, Nonlinear system theory, Modeling
Abstract: In this paper, an approach based on approximation of Hamiltonian system is proposed to stabilize an under actuated Hamiltonian system. Interconnection and damping assignment passivity based (IDA-PBC) method is a well-known approach to this problem but it requires solving nonlinear partial differential equations (PDE), which is not an easy task. The proposed approach has been inspired by the simplicity of solving these PDE’s for the separable case. So an approximate model based on separable Hamiltonian system is formed. The approximate model is constructed by approximating the generalized inertia matrix. This approximation is based on using a linear combination of basis functions like radial ones where constant inertia matrices form the coefficients. Using the approximated model, the new matching conditions are obtained for the IDA-PBC method as a set of linear partial differential and a set of linear equations. Therefore, this approach requires solving linear PDEs which should have a common solution, along with solving a set of linear equations to determine the control rules corresponding the energy shaping and damping assignment. With the proposed approach, instead of solving nonlinear PDEs, linear ones are solved, thus an easier way is given. To illustrate the effectiveness and the appropriateness of the proposed method, the pendulum on a cart problem is considered.

Keywords: Stability of nonlinear systems, Nonlinear system theory, Lyapunov methods
Abstract: The Controlled Lagrangian method is a strategy for the design of control systems for a class of Lagrangian systems. This method has resolved the stabilization problem of some well–known underactuated mechanical systems, including an inverted pendulum on a force-driven cart benchmark. This paper goes deeply into the analysis of this control system by studying in detail asymptotic stability invoking the Barbashin–Krasovskii’s theorem and giving an explicit novel estimate of the domain of attraction. As a consequence, an estimate of the domain of attraction that resolves the practical motivated issue of maintaining the travel of the cart within prescribed physical limits of displacement is obtained. Numerical simulations are presented to illustrate these results.

Keywords: Stability of nonlinear systems, Lyapunov methods
Abstract: The first step toward development a ``nonsmooth'' version of Speed-Gradient (SG) method is made. As a basis for formal approach the Hadamard subdifferential and set-valued analysis are chosen. Nonsmooth versions of SG-algorithm in differential and finite form are formulated. Conditions for the control goal achievement are proposed. The results are illustrated by an example of asymptotic minimization of the max-norm for a second order linear system.

Keywords: Agents and autonomous systems, Agents networks
Abstract: In this paper a source seeking method for multi-agent systems organized with the Leader-Follower scheme is studied. Our objective is to develop a controller for the headings of the agents. The group of agents is characterized by an initial leader, which steers all the agents towards an initial given heading. Another agent, an active follower, can take on the role as leader if it gets satisfactory measures from the environment. If the active follower becomes leader, it steers the whole group towards the source present in the field. We focus on a 2D case, and simulation results are reported to illustrate and validate theoretical results.

Keywords: Agents and autonomous systems, Concensus control and estimation, Stability of nonlinear systems
Abstract: In the present paper, the Leader-Following consensus problem is investigated and sufficient conditions are given for the solvability of the problem, assuming that the agents are described by a nonlinear dynamics incrementally homogeneous in the upper bound.

Keywords: Agents and autonomous systems, Control over networks, Optimal control
Abstract: In a crowd model based on leader-follower interactions, where positions of the leaders are viewed as the control input, up-to-date solutions rely on knowledge of the agents' coordinates. In practice, it is more realistic to exploit knowledge of statistical properties of the group of agents, rather than their exact positions. In order to shape the crowd, we study thus the problem of controlling the moments instead, since it is well known that shape can be determined by moments. An optimal control for the moments tracking problem is obtained by solving a modified Hamilton-Jacobi-Bellman (HJB) equation, which only uses the moments and leaders' states as feedback. The optimal solution can be solved fast enough for on-line implementations.

Keywords: Agents and autonomous systems, Cooperative control, Maritime
Abstract: This paper considers straight-line path following for inhomogeneous formations with underactuated agents. The formation can be comprised of agents with different dynamics that are each affected by a different unknown environmental disturbance. Formation path following is achieved using a twofold strategy consisting of a guidance law to steer each vessel to a predefined path and a decentralised nonlinear formation control law utilising local information only to synchronise the agents position along the path such that a desired formation is achieved. The resulting closed-loop error dynamics consisting of the path-following error dynamics and formation error dynamics is analysed using theory for feedback-interconnected systems. The origin of the closed-loop error dynamics is shown to be uniformly globally asymptotically stable. The control strategy is validated with simulation results in a case study.

Keywords: Agents and autonomous systems, Delay systems, Flexible structures
Abstract: The paper brings together two different approaches for control of chain of oscillatory lumped-parameter multi-agent systems. Namely, the multi-mode zero-vibration input shaper and the wave-absorbing controller are recalled and the similarities and links between them are broadly discussed. The special case of identical agents with a double-integrator character is at the focus throughout the paper. The report reveals that the two approaches are closely related in spite of the fact that they differ significantly in all aspects, from motivation through computational algorithms to target implementation. In addition, the presented numerical results, mostly based on numerical simulations at this moment, show that the two methods can be combined together, to take advantage of both an appropriate initial excitation of the system by the input shaper and of increased robustness coming from the wave-absorber feedback architecture. Such a combined control law is based on a special property of the multi-mode zero vibration input shaper - namely the convergence of its impulse response, as the number of agents increases, to a double bell-shaped function.

Keywords: Agents and autonomous systems, Intelligent systems, Transportation systems
Abstract: This paper presents a computational model capable of improving the action policies for a well-defined domain. Each action policy is represented as a driving plan P, which is composed of a number of actions {a1, ... an}. These actions can be used to move a train in a stretch of railroad Sti. The plans are elaborated using a CBR approach and reusing previous solutions and learning from plans. The CBR cycle is divided in three agents that act collaboratively to build or run P, namely: Planner, Executor, and Memory. The Planner agent generates P. Executor agent is responsible for revise and apply the actions of P. During the execution, P may undergo several adjustments depending on multiple circumstances, such as environmental conditions. The modified plan P’ returns to its origin end to integrate the local case base, managed by the Memory agent. This approach was evaluated on the following criteria: (i) fuel consumption, (ii) accuracy of case retrieval, and (iii) efficiency of adaptation task and application of adapted cases in real-world scenarios. The inclusion of new experiences reduced efforts Planner and Executor in their tasks, and a reduction in fuel consumption. In addition, the model shows that the increase in diversity in the case base increases the reuse of experiences in objectives-scenarios.

Keywords: Electrical power systems, Predictive control for linear systems
Abstract: In this paper, a model predictive control scheme is proposed for the load frequency control (LFC) problem of a two-area deregulated power system with measured (contracted) and unmeasured (uncontracted) loads. The proposed controller is designed by posing the problem as a tracking one with states and input constraints representing generation rate constraints and input limits respectively. The simulation results obtained from implementing the proposed scheme showed its effectiveness in handling the LFC problem.

Keywords: Electrical power systems, Stability of nonlinear systems, Nonlinear system theory
Abstract: Synchronverters are grid-friendly inverters that mimic the operation of conventional synchronous generators. In this paper, the non-linear stability of the synchronverter in the sense of boundedness is investigated and proven for the first time. To this end, initially, the complete non-linear model of the synchronverter is obtained and then the field-excitation current loop of the synchronverter is implemented using a bounded integral control (BIC) structure, as proposed by the authors in the literature. While maintaining the original synchronverter operation near the rated value, the BIC additionally guarantees that the field-excitation current will remain bounded in a given range. Using non-linear analysis and input-to-state stability theory, it is proven that the frequency dynamics will remain bounded which leads to a bounded synchronverter voltage and finally results in the stability of the closed-loop system in the sense of boundedness. Extensive simulation results verify that the proposed synchronverter with the BIC approximates the behavior of the original synchronverter near the rated value with a guaranteed bounded performance.

Keywords: Electrical power systems, V&V of control algorithms, Modeling
Abstract: This paper presents the MATLAB simulation framework, DiSC, for verifying voltage control approaches in power distribution systems. It consists of real consumption data, stochastic models of renewable resources, flexible assets, electrical grid, and models of the underlying communication channels. The simulation framework makes it possible to vali- date control approaches, and thus advance realistic and robust control algorithms for distribution system voltage control. Two examples demonstrate the potential voltage issues from penetration of renewables in the distribution grid, along with simple control solutions to alleviate them.

Keywords: Electrical power systems, Large-scale systems, Robust control
Abstract: This paper deals with a dynamic pricing via the H-infinity control considering uncertainties in market participants' behavior. The dynamic pricing is a decision procedure of an electricity price based on power demand and supply information from selfish power consumers and generators. However, since market participants have uncertainties in their behavior, the price decision procedure is required to have robustness against these uncertainties for stable operation of power systems. Then, in this paper, we propose a novel price decision procedure via the H-infinity control and also show the effectiveness of our proposed price decision method in simulation results.

Keywords: Electrical power systems, Optimization algorithms, Decentralized control
Abstract: Plug-in electric vehicles (PEVs) are becoming increasingly popular because of the environmental and economic benefits. However, high penetration of PEVs may overload the distribution network. In this paper, we propose a decentralized PWM-based algorithm to coordinate PEV charging. We first formulate the PEVs charging coordination problem as an optimization problem, with the objective to flatten the total demand curve as much as possible. Then, we design the control algorithm in two stages. In the first stage, we adopt the the water-filling-based algorithm proposed in our previous study, assuming the charging rate of PEVs takes a continuous value. In the second stage, the assumption is dropped by utilizing the pulse-width modulation (PWM) principle. The moving horizon idea is also introduced to alleviate the errors due to inaccurate forecast and quantization, as well as to tackle the random arrival time of PEVs. Moreover, each PEV only needs to calculate its own power allocation, and hence its implementation requires low computational capacity. Numerical simulations are given to demonstrate the effectiveness of our algorithm.

Keywords: Electrical power systems, Optimization algorithms, Decentralized control
Abstract: The economic dispatch problem (EDP) is of vital importance in the operation and control of power systems. In this paper, we consider the extended EDP that takes into account transmission losses and propose a distributed algorithm based on the average consensus algorithm and the bisection method. We assume that the total transmission losses can be represented by the B matrix loss formula, and the communication network between generators (nodes) is a connected undirected graph. A leader node is used to broadcast the total demand information by communicating with merely a small part of the nodes. Our algorithm is distributed in the sense that the nodes conduct local computations and communicate with their neighbors. Simulation results are given to show the performance of our algorithm.

Keywords: Mechatronics, Nano systems, Aerospace
Abstract: In this paper, an integral plus double integral synchronization controller is developed for multiple piezoelectric actuators through a state feedback approach. Dynamic modeling of the piezoelectric nanopositioner is conducted through both linear and nonlinear phenomenological models. The linear and nonlinear models are then used along with the experimental system to perform hardware in the loop (HITL) simulations of the synchronization controller for a parallel three-axis nanopositioning system. This would allow the piezoelectrics to form the basis of an ultra-precise 2-D Fabry-Perot interferometer as the gap spacing of the device could be controlled at the nanometer level.

Keywords: Mechatronics, Nano systems
Abstract: The Butterworth filter is known to have maximally flat response. Incidentally, the same response is desired in precise positioning systems. This paper presents a method for obtaining a closed-loop Butterworth filter pattern using common control schemes for positioning applications, i.e. Integral Resonant Control (IRC), Positive Position Feedback (PPF), and Positive Velocity and Position Feedback (PVPF). Simulations show a significant increase in bandwidth over traditional design methods and verify the desired pole placement is achieved. Experiments are performed using a two-axis serial kinematic nanopositioning stage. The results show a significant improvement in bandwidth and increased positioning accuracy, specifically at the turn-around point. This allows a greater portion of the scan to be used and improved positioning accuracy at high scanning speeds.

Keywords: Mechatronics, Modeling, Flexible structures
Abstract: As shown in previous work, there exist several options for modeling of flexible mechanical systems that are readily applicable for the design of observer-based closed-loop control strategies. Especially, finite element techniques, which are derived by means of an early-lumping approach, provide a good compromise between accurate modeling and real-time capability of the resulting control and estimation procedures. However, an increase of the degrees of (polynomial) ansatz functions for the representation of characteristic quantities such as bending deflections as well as an increase of the number of finite elements lead to rapidly growing system orders. On the one hand, this order increase brings the drawback that an excessive computational effort may be required. In the worst case, this results in a loss of real-time capability. On the other hand, it is also possible that system models are obtained which contain information that is redundant for a feedback control design. The latter holds for cases in which eigenvalues are included in finite-dimensional state-space representations with features of the system dynamics that are sufficiently faster than the available actuators. Hence, order reduction techniques become necessary in practical control tasks. In this paper, suitable modeling and validation approaches are described which allow for limiting the system order to a value that still guarantees sufficient accuracy for the control task at hand. Representative simulation results are discussed in this paper which are the basis for a future experimental validation.

Keywords: Mechatronics, Optimal control, Robotics
Abstract: This paper proposes a method to determine the optimal value of design parameters in robots driven by variable-stiffness actuators. The method consists of setting up a nonlinear optimization problem, the solution of which determines the optimal control sequence, and, at the same time, the optimal values of the parameters. As a case study, we analyze a ball-throwing problem for a two-link elbow manipulator actuated by antagonistic quadratic springs, and show results for different configurations. Even if similar methods have already been proposed, mainly in process control, this approach is novel when applied to robots, and could lead to an overall improvement of their design, exploiting numerical optimization tools, which, in the last years, have become faster and more reliable.

Keywords: Mechatronics, Predictive control for linear systems, Filtering
Abstract: The dynamic displacements of micro vibration isolation systems still need to be suppressed because the precision accuracies in Hi-tech manufacturing industries have currently progressed to nanometer. In this study, the dynamic behavior of a vibration isolation system using a negative stiffness controller is further improved by additional acceleration feedbacks. This improvement is confirmed theoretically and experimentally; however, it causes the system rather costlier when a servo accelerometer is used to measure acceleration. Thus to improve the dynamic behaviors of a vibration isolation system using acceleration feedback without increase of cost, low-cost MEMS (Micro Electrical Mechanical System) accelerometers are used in the developed experimental system. Nevertheless, the acceleration signals measured by a MEMS accelerometer are typically noisy. To overcome this difficulty, a Kalman-filter estimated acceleration feedback is considered in this study.

Keywords: Mechatronics, Robotics, Servo control
Abstract: In this study, a new servo control system based on discrete-time state feedback approach is developed for overhead cranes to provide high performance trajectory tracking and load swing suppression as the main two objectives. Inspired by the idea of independent joint control in robot manipulator control field, a new model is derived in which the overhead crane actuators are considered as the main plant. The overhead crane nonlinearities are then treated as disturbances acting on each actuator and compensated via computed torque control in feedforward action. A new load swing control is designed and integrated to the servo controller through modifying reference trolley acceleration. A series of practical results is provided to indicate the stability and high performance of the proposed control system.

Keywords: Constrained control, Optimization algorithms, Aerospace
Abstract: This paper introduces a new algorithm for atti- tude motion planning, Constrained Attitude Guidance (CAG) problem, in the presence of angular rate constraints and conic exclusion regions (pointing constraints). The CAG problem is solved by considering only the quaternion kinematics in the formulation and using constraints on quaternions and its time derivatives to indirectly apply bounds on the angular rates and accelerations. The CAG formulation makes use of Mixed Integer Convex Programming (MICP) in order to impose, approximately, the unity constraint on the quaternion magnitude, where the approximation accuracy can be set to a desired accuracy. The solution complexity of the MICP formulation increases exponentially with the number of binary variables that are used to impose the unit norm constraint on the quaternion. Since this number is independent of the number of exclusion pointing constraints, the solution approach has favorable complexity in terms of the number of pointing constraints. The paper also provides a numerical example that incorporates both angular rate and pointing constraints.

Keywords: Constrained control, Linear parameter-varying systems, Energy systems
Abstract: This paper proposes a pragmatic solution to solve input and state constrained control problems. Taking benefits from a two-layer hierarchical architecture, in particular by working at a different period at each level, the general idea is to combine an explicit LPV controller ensuring the regulation task, and a predictive control at the upper level to comply with the active constraints. In practice, the two layers are connected as the external loop drives the varying parameter of the inner loop. The proposed scheme is well suited mainly with control problems whose constraints violation risks may be predicted sufficiently in advance. The energy management of a hybrid vehicle is finally considered to illustrate the applicability.

Keywords: Electrical power systems, Predictive control for linear systems, Stochastic control
Abstract: Robust programs with modulated uncertainty sets are problems in which the uncertainty sets are treated as optimization variables. In many applications, these uncertainty sets can be interpreted as reserve capacities for which rewards are offered. One example is the provision of frequency reserve capacities to the power grid by demand-side resources. This paper studies the case in which the reserves are offered by commercial buildings. We determine the optimal size of the reserve capacity set such that the buildings can follow any reserve demanded within the set, while guaranteeing their comfort constraints. Since the actual reserve demands are uncertain, we interpret the reserve demands as random variables and formulate a chance-constrained program to ensure comfort constraints with high probabilities. By restricting the class of policies to affine decision rules and applying the scenario approach to approximate the chance constraints, we obtain a tractable convex problem. We compare our chance-constrained framework to previous work with robust comfort constraints and demonstrate its efficacy based on a numerical case study.

Keywords: Hybrid systems, Optimal control, Robotics
Abstract: This paper proposes a method for automatic generation of time-optimal robot motion trajectories for the task of collecting and moving a finite number of objects to particular spots in space, while maintaining predefined temporal logic constraints. The continuous robot dynamics change upon an object pick-up or drop-off. The temporal constraints are expressed as syntactically co-safe Linear Temporal Logic (scLTL) formulas over the set of object and drop-off sites. We propose an approach based on constructing a discrete abstraction of the hybrid system modeling the robot in the form of a finite weighted transition system. Then, by employing tools from automata-based model checking, we obtain an automaton containing only paths that satisfy the specification. The shortest path in this automaton is found by graph search and corresponds directly to the time-optimal hybrid trajectory. The method is applied to a case study with a mobile ground robot and a case study involving a quadrotor moving in an environment with obstacles, thus reflecting its computational advantage over a direct optimization approach.

Keywords: Computational methods, Optimal control, Optimization
Abstract: This paper presents a parallel collocation algorithm for the solution of a two-point boundary value problem (BVP) that involves index-1 differential-algebraic equations (DAEs) and inequality constraints due to complementarity conditions. BVP-DAEs of this type arise from the indirect approach to the solution of optimal control problems that control variable inequality constraints. In the collocation method presented here the differential and algebraic variables of the BVP-DAEs are approximated using piecewise polynomials on a mesh that may be nonuniform. A Newton interior point method is used to solve the collocation equations, and maintain feasibility of the inequality constraints. The implementation of the algorithm involves parallel evaluation of the collocation equations, parallel evaluation of the system Jacobian, and parallel solution of a boarded almost block diagonal (BABD) system to obtain the Newton search direction. A numerical example shows that the parallel implementation provides significant speedup when compared to a sequential version of the algorithm, and when compared to a direct method.

Keywords: Predictive control for linear systems, Constrained control, Control over networks
Abstract: We present two event-triggered MPC laws that do not require to solve a QP in every time step but only upon certain events. We prove one of the control laws results in exactly the same closed-loop behavior as classical MPC. The second control law requires even fewer QPs per time. It is suboptimal w.r.t. the MPC cost function, but still results in asymptotically stable closed-loop behavior. We illustrate the event-triggered MPC laws with two examples.

Keywords: Computer aided control design, Computational methods, Reduced order modeling
Abstract: In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured model reduction using a subgradient optimization algorithm. We briefly present the syntax for the toolbox and its features. Finally, we demonstrate the applicability of various model reduction methods in the toolbox on a structured mass-spring mechanical system.

Keywords: Model/Controller reduction, Nonlinear system theory
Abstract: In this paper, we present a novel balancing method for nonlinear systems in the contraction framework. We define two energy functions via variational systems. These novel controllability and observability functions can be used for model reduction of nonlinear systems. We analyze their properties, use for balancing, and application to model order reduction.

Keywords: Feedback linearization, Distributed parameter systems, Output feedback
Abstract: A finite-dimensional dynamic compensator for the Schlögl model is designed. The equation of interest is a parabolic partial differential equation with cubic reaction term. Based on model reduction methods for linear infinite-dimensional control systems, a finite-dimensional linear compensator is obtained and shown to be locally stabilizing the original nonlinear problem. Theoretical results are confirmed by a numerical example.

Keywords: Reduced order modeling, Differential algebraic systems, Computational methods
Abstract: We propose a model reduction technique for quadratic-bilinear descriptor systems. The approach involves approximating the system by a bilinear descriptor system using Carleman bilinearization [1]. It is shown that, by assuming a particular structure of the matrix pencil, the bilinearization process preserves the structure of the matrix pencil in the bilinearized system. Further, we extend the use of the bilinear iterative rational Krylov algorithm (B-IRKA) [2] to descriptor systems to identify a locally H₂-optimal reduced-order system for the bilinearized system under the assumption that the H₂ norm of the system exists. Applications to the simulation of a nonlinear RC circuit and a lid-driven cavity flow are presented to illustrate the proposed methodology.

Keywords: Distributed parameter systems, Model/Controller reduction
Abstract: We show that the Gramians of a control system with an analytic semigroup, control and observation operators that are not too unbounded and which have finite-dimensional input and output spaces have singular values which decay exponentially in the square root. As a corollary it is shown that the Hankel singular values of such control systems also decay exponentially in the square root. Another corollary shows that solutions of algebraic Riccati equations for such systems also have singular values which decay exponentially in the square root.

Keywords: Model/Controller reduction, Hybrid systems
Abstract: The problem of model reduction by moment matching for LTI systems driven by specific exogenous signals is tackled in the case of discontinuous input signals. In particular, we consider a class of piecewise-continuous signals that can be generated as the output of suitably defined linear hybrid systems in the presence of periodic jumps. The proposed class of reduced-order models, which are given in terms of linear time-varying hybrid systems, is constructed by borrowing techniques from the theory of output regulation for linear hybrid systems. The resulting approach combines rather mild constructive assumptions, requiring only a generically satisfied non-resonance condition, with a significant reduction of the state dimension. In fact, a reduced-order model with state dimension matching the number of outputs can be obtained regardless of the number of original states. Finally, the performance of the methodology is assessed by means of numerical simulations.

Keywords: Stochastic control, Optimization algorithms, Randomized algorithms
Abstract: The problem considered in this paper is the minimization of expected cumulative losses in a stochastic system. The losses over time horizon are formed by the values of an unknown loss function at the consecutive jump times of a renewal process. The loss is assumed to be a convex function of a vector parameter, and the only available information is represented by an oracle which provides stochastic subgradients of the loss function. The control objective is to minimize the expected cumulative loss over a given convex compact set. We propose an adaptive mirror descent algorithm and prove an explicit upper bound for the related regret, which is the difference between the expected cumulative losses and the minimum. Finally, to exemplify the efficiency of the method, we consider the problem of minimization of the expected cumulative losses over the standard simplex by handling a stream of losses arriving by the Erlang process, and we discuss the simulation results.

Keywords: Stochastic control, Hybrid systems, Randomized algorithms
Abstract: This paper addresses the computational issues involved in the solution to an infinite-horizon optimal control problem for a Markov Decision Process (MDP) with a continuous state component and a discrete control input. The optimal Markov policy for the MDP can be determined based on the fixed point solution to the Bellman equation, which can be rephrased as a constrained Linear Program (LP) with an infinite number of constraints and an infinite dimensional optimization variable (the optimal value function). To compute an (approximate) solution to the LP, an iterative randomized scheme is proposed where the optimization variable is expressed as a linear combination of basis functions in a given class: at each iteration, the resulting semi-infinite LP is solved via constraint sampling, whereas the number of basis functions is progressively increased through the iterations so as to meet some performance goal. The effectiveness of the proposed scheme is shown on a multi-room heating system example.

Keywords: Stochastic systems, Optimal control
Abstract: In this paper we extend the guaranteed cost control approach for nonlinear quadratic systems (NLQSs), developed by the same authors in some recent papers, to the stochastic framework. In particular, we consider a stochastic NLQS in the It^o's form and provide a sufficient condition for the existence of a state feedback controller guaranteeing, with a certain risk factor α in [0,1), that the closed loop system satisfies, for any initial condition belonging to a given polytopic set, an assigned bound for a given quadratic cost; the condition requires to solve a feasibility problem constrained by linear matrix inequalities. The proposed theory is then illustrated by an example concerning the design of optimal strategies for the removal of malicious software in computer networks.

Keywords: Stochastic systems, Hybrid systems, Stochastic control
Abstract: In this paper, we propose an efficient algorithm to find an optimal control policy in a discrete-time hidden mode stochastic hybrid system, which is a special case of partially observable discrete-time stochastic hybrid systems in which only discrete states are hidden. Many human-centered systems can be modeled as such systems, in which the intent of the human operator is unknown and can be modeled as the hidden mode. In the literature, the optimal control problem of hidden mode stochastic hybrid system is known to have high computational complexity due to the continuous state space. In this paper, we will tackle this computational challenge by using local quadratic functions to approximate the optimal expected reward, which does not have a closed-form expression in general. We will show the efficacy of our proposed method, and the significant improvement in the computational time.

Keywords: Stochastic systems, Stability of linear systems, LMI's/BMI's/SOS's
Abstract: In this paper we investigate the stochastic finite-time stability (SFTS) problem for linear time-varying systems. The system under consideration is described by an Ito type differential equation and the Ito differentiation rule is exploited to derive conditions for SFTS. The main contribution of the paper is that we use an approach based on time-varying quadratic Lyapunov functions, which allow us to obtain less conservative conditions than the time-invariant Lyapunov functions commonly used in the literature. More specifically, we obtain a sufficient condition based on the solution of a generalized Lyapunov differential equation (GLDE) and a sufficient condition requiring the solution of a feasibility problem involving a differential LMIs (DLMI) constraint. We shall show that the DLMI based condition is less conservative and is useful to develop a sufficient condition for stochastic finite-time stabilizability via state feedback; on the other hand the GLDE condition is more efficient from the computational point of view. Numerical examples illustrate that the proposed approach attains less conservative results than those obtainable with the existing literature.

Keywords: Stochastic systems, Modeling
Abstract: In this paper, we consider the problem of scheduling a number of patients for visits to a cancer infusion room throughout a regular day. We suggest the use of high and low patient acuity indicators to account for punctuality and service uncertainties in the scheduling process. These supportive classifications can be used easily by schedulers to allow more efficient, individualized service. Based on patient acuity data and clinical observations, we propose two intuitive though somewhat conflicting scheduling guidelines on a qualitative basis and argue their benefits. Due to the analytic intractability of the primal scheduling problem, we make use of analogies with standard queueing theory and strings of interconnected dynamic systems to introduce two separate surrogate problems allowing analysis of the effects resulting from our scheduling rules on the operation of the infusion room.

Keywords: LMI's/BMI's/SOS's, Optimization algorithms, Distributed parameter systems
Abstract: INTSOSTOOLS is a plug-in for the MATLAB toolbox SOSTOOLS for the formulation of optimization problems with constraints of the form of one-dimensional integral inequalities. For polynomial problem data, semidefinite programming can be used to solve the underlying optimization problems. This paper details a method for checking integral inequalities and shows how to use INTSOSTOOLS to cast optimization problems with integral constraints and linear objective functions. Two examples illustrate the potential of the proposed method and of the developed software.

Keywords: Lyapunov methods, Autonomous robots, Robust control
Abstract: Remotely operated vehicles equipped with a robotic manipulator are utilized in several underwater/deep sea applications. Control of these type of systems are mostly provided by obtaining the proper position for the end effector of robotic manipulator which constitutes the desired motion for remotely operated vehicle. This situation makes the control of robotic manipulators is really important subject for underwater applications. In this work, we study tracking control of a one degree-of-freedom rigid link in a cross flow. Systems operating at underwater (including this one) are hard to model accurately, and as a result their models include several uncertainties. To reject these modeling uncertainties and external ones, two robust controllers are proposed. Stability of the closed-loop system and the asymptotic convergence of the tracking error are proven mathematically. Numerical simulations are performed to demonstrate the viability of the proposed controller.

Keywords: Lyapunov methods, Observers for linear systems, Delay systems
Abstract: In this work, the H-infinity filtering problem for fractional-order time-varying-delay systems is investigated. In the absence of disturbances, the observer state should asymptotically converge to the actual state. On the other case, when the system is subject to disturbances, the H-infinity observer designed must minimize the effect of disturbances on the estimation error. On the basis of the indirect Lyapunov approach, the stability condition is given in Linear Matrix Inequality (LMI) formulation. Finally, a numerical example is presented to illustrate the performances of the proposed observer.

Keywords: Lyapunov methods, Stability of nonlinear systems
Abstract: This paper considers stabilization of fully actuated rigid-body attitude dynamics in the absence of angular velocity measurements and presents new robustness results to bounded unknown external disturbance torques. In particular, it is assumed that only body orientation is measured in the form of a unit-quaternion signal. It is well known that the passivity properties of the dynamics allows design of velocity-free controllers using a first-order stable filter driven by measured states. When external disturbance torques are taken into account, however, the robustness properties of these passivity-based output feedback controllers cannot be readily analyzed because the Lyapunov-like function from which the controller is derived has a time-derivative that is only negative semidefinite, and therefore non-strict. This obstacle is circumvented through a new partial-strictification approach which ultimately allows the characterization of robustness properties for this closed-loop system.

Keywords: Lyapunov methods
Abstract: The paper presents new results for the robust guaranteed cost control problem for a nonlinear neutral system having infinite delay with a given quadratic cost function. A delay dependent stability criterion, based on a model transformation technique, is proposed. A state feedback control law is then designed using the Razumikhin stability approach and the Lyapunov matrix equation to ensure not only the closed-loop systems robust stability but guarantee that the closed-loop cost function value remains within a specified bound. The problem of designing the optimal guaranteed cost controller is also given in terms of inequalities. An example illustrates the theoretical results.

Keywords: Optimization, Lyapunov methods, Electrical power systems
Abstract: In this paper we propose a modified primal-dual gradient dynamical system to solve non-convex optimal power flow problems. The modified gradient dynamics maintains the naturally distributed structure and it has isolated equilibrium points as the primal and dual optima. Under mild conditions we show the locally asymptotic stability of the modified gradient dynamics. Simulations on the IEEE 14-bus benchmark system are provided to demonstrate the effectiveness of the proposed approach.