Keywords: Energy systems, Mechatronics, Optimization
Abstract: The focus of this work is on addressing and solving the mixed-objective optimization problem for the operation of a wind farm, which considers both power maximization and mechanical load reduction. The proposed strategy provides the opportunity to operate the wind farm in different ways, depending on whether maximizing power production or reducing turbines wear is more relevant. We incorporate the power maximization objective by considering the mean value of the produced power; the load reduction is divided in two cases, i.e., extreme loads and fatigue damage, incorporated via the thrust force and the thrust force deviations in the cost function, respectively.

Keywords: Electrical power systems, Concensus control and estimation, Optimization
Abstract: The prevalent distributed generation resources warrant reconsideration on how their coordination is achieved. In this paper, we particularly focus on how to enhance secondary frequency control by exploiting peer-to-peer communication among the resources. We design a control framework based on a consensus-plus-global-innovation approach. The control signals of distributed resources are updated in response to a global innovation (utilizing the area control error signal), and additional information exchanged via communication among neighboring resources. We show that such a distributed control scheme can be very well approximated by a proportional-integral controller and stabilizes the system. Moreover, since our scheme takes advantage of both the global and neighboring information, simulation results demonstrate that our scheme stabilizes the system significantly faster than the conventional automatic generation control framework. In addition, our control scheme asymptotically achieves the cost effectiveness.

Keywords: Electrical power systems, Modeling, Predictive control for linear systems
Abstract: This paper summarizes comprehensively the work in four recent PhD theses from the Technical University of Denmark related to Economic MPC of future power systems. Future power systems will consist of a large number of decentralized power producers and a large number of controllable power consumers in addition to stochastic power producers such as wind turbines and solar power plants. Control of such large scale systems requires new control algorithms. In this paper, we formulate the control of such a system as an Economic Model Predictive Control (MPC) problem. When the power producers and controllable power consumers have linear dynamics, the Economic MPC may be expressed as a linear program. We provide linear models for a number of energy units in an energy system, formulate an Economic MPC for coordination of such a system. We indicate how advances in computational MPC makes the solutions of such large-scale models feasible in real-time. The system presented may serve as a benchmark for simulation and control of smart energy systems and we indicate how advances in computational MPC.

Keywords: Optimal control, Modeling, Energy systems
Abstract: This paper studies the supply-demand matching problem in the hierarchical market-based structure of the Universal Smart Energy Framework. A mismatch between the forecasted and the actual load in smart electricity grids can arise due to the intermittent nature of the renewable energy sources. To minimize this deviation, we propose a distributed model predictive controller, in which prosumers equipped with flexible appliances make control decisions based only on local information, also taking the distribution network capacity limitations into account. A small-scale simulation illustrates the feasibilty of the method.

Keywords: Electrical power systems, Distributed control, Control over networks
Abstract: Recently we have been exploring the role of passivity and the internal model principle in power network control in the presence of uncertainties due to unmeasured demand and supply. In this work we continue this line of research and extend our results to include more complex dynamics at the generation side. Namely, we study frequency stabilization by primary control and frequency regulation by optimal generation control, where we additionally incorporate second-order turbine-governor dynamics. The power network is represented by the structure-preserving Bergen-Hill model. Distributed controllers that require local frequency measurements are proposed and are shown to minimize the generation costs. Asymptotic convergence is proven when the generators satisfy a local matrix condition. The effectiveness of proposed controllers is demonstrated in a case study.

Keywords: Energy systems, Power plants, Modeling
Abstract: Wake flows and turbine dynamics mean that wind farms are very complex physical systems. This paper presents a simplified engineering model which allows advanced wind plant sector management to be rapidly optimised, trading off energy production and turbine loading to minimise the cost of energy. A simple illustrative case study indicates the scope for significant benefits compared to doing nothing or simply turning off the most wake-affected turbines. The method also allows grid ancillary service provision such as curtailment to be managed for minimum fatigue load accumulation.

Keywords: Computational methods, Network analysis and control, Biomolecular systems
Abstract: Although Chemical Reaction Networks (CRNs) form a rich class of nonlinear systems that can exhibit wide range of nonlinear behaviours, many common examples are observed to be asymptotically stable regardless of the kinetics. This paper presents the recently uncovered class of Graphically Stable Networks (GSNs) which is characterized by the existence of a robust Lyapunov function defined in the reaction coordinates. Subject to mild conditions, the existence of these functions guarantees asymptotic stability of a network regardless of the specific form of kinetics. Construction methods for these functions are provided and illustrated by examples.

Keywords: Control over networks, Lyapunov methods, Large-scale systems
Abstract: In this tutorial presentation we focus on the construction of Lyapunov or storage functions for large-scale networked control systems (NCSs) in which sensors, controllers and actuators are connected via multiple (local) communication networks which operate asynchronously and independently of each other. Within each packet-based communication network only one node can communicate at a given transmission time (requiring communication protocols) and the transmission intervals and delays may vary over time. These artefacts cause network-induced communication errors in the overal closed-loop system and can be detrimental for stability and performance. For these NCSs we provide explicit constructions of Lyapunov functions by modelling the large-scale NCS as an interconnection of a finite or even an infinite number of hybrid subsystems, and combining "local" Lyapunov functions for the controlled dynamics (including network-induced errors) and the protocols in a systematic manner. These constructions lead to the numerical computation of maximum allowable transmission intervals (MATIs) and maximum allowable delays (MADs) for each of the individual networks. The availability of the Lyapunov or storage functions guarantee properties such as global asymptotic or exponential stability, input-to-state stability (ISS) and Lp-stability for the large-scale NCS. Interestingly, the control performance expressed in terms of ISS and Lp-gains can be traded with the network parameters (MATIs and MADs). Hence, tradeoffs can be made between the quality-of-control of the overal hybrid system and the required quality-of-service of the underlying communication infrastructure. Also event-triggered communication schemes will be shortly discussed. The results are illustrated with an example of vehicle platooning.

Keywords: Automotive, Cooperative control, Lyapunov methods
Abstract: A shared-control algorithm for the kinematic model of a rear-wheel driving car is presented. The design of the shared-controller is based on a hysteresis switch and its properties are established by a Lyapunov-like analysis. The shared-controller guarantees the safety of the car in both predefined, static environments and time-varying environments. The effectiveness of the controller is verified by two studies.

Keywords: Automotive, Delay systems, Identification
Abstract: A new method is proposed for driver reaction time (delay) and parameter estimation using a generic lateral model that is expressed in terms of the steering angle, yaw rate and lateral lane offset. The idea behind the presented method is to reformulate the original driver model with an over-parametrized one and then use the L1-regularization method to enforce sparsity and thereby estimate the delay together with the parameters of the original model. A sequential algorithm is then presented to obtain better estimates of the parameters with a model in which the delay is fixed.

Keywords: Automotive, Modeling, Model validation
Abstract: The paper tackles a problem of modeling a vehicle lateral control performed by human driver. Nowadays, the modeling of driver behavior is a frequently suggested research topic and a lot of different models exist. Here, the steering control models, available in literature are presented and discussed. The similarities in different models are shown and a generalized model is proposed, merging the major different models into the same mathematical structure. Finally, the correspondence of a model is validated using real drivers data collected on a driving simulator

Keywords: Automotive, Randomized algorithms, Autonomous systems
Abstract: This paper describes a data-driven Randomized Model Predictive Control (MPC) approach toward autonomous racing of miniature cars. The main challenge in autonomous racing is to drive as fast as possible, without actually exiting the track. Designing such controllers is a challenging task, since (i) the models of the cars are not entirely accurate, and (ii) the time to compute the control inputs is limited to tens of milliseconds. The current practice is to resort to standard MPC, where the safety-related constraints are tightened manually. In this paper, we propose an alternative method based on Stochastic MPC, which naturally introduces robustness by design. We approximate the Stochastic MPC problem by means of randomization, implemented as a sparse Randomized MPC problem. We show that the resulting quadratic program can be solved in the range of milliseconds. Moreover, the sparse Randomized MPC formulation can be interpreted as a standard MPC problem whose constraints are, based on collected data, automatically tightened. We show experimentally that the proposed controller can outperform currently implemented controllers. Our results suggest that Randomized MPC is an attractive alternative to standard controllers, due to its ability to introduce robustness without sacrificing performance.

Keywords: Automotive
Abstract: This paper presents a design for a nonlinear rear-wheel steering (RWS) controller tailored to urban demands. The proposed yaw rate controller structure uses the method of input-output linearization (IOL). Instead of classical feedback linearization, states are obtained from a controller design model excited by current requested control input. The linearized model is mainly driven by reference yaw jerk, thus ensuring quick reactions. A proportional-derivative (PD) feedback control input is applied for stabilization. The input affine controller model covers unsteady-state tire behavior. Model validation has been performed using an experimental vehicle. A sports vehicle has been selected to set the reference trajectories. Control performance is demonstrated through a complex validated simulation model.

Keywords: Autonomous systems, Automotive, Electrical power systems
Abstract: This paper shows the advantage of autonomous driving systems from testing point of view in order to enhance the performance of a racing car with respect to the use of driver assistant systems (DAS). Specifically, for the development of such systems it is necessary to perform parameter studies based on repeatable driving maneuvers. Even well trained test drivers have limited ability to achieve the required repeatability of the vehicle behavior, especially when driving at the stability limit of the vehicle. The autonomous vehicle guarantees the required position accuracy for the driving maneuvers even at high lateral acceleration with different controller settings of Active Yaw Control under real conditions. Such parameter studies are usually done using simulation tools that need very precise nonlinear tire characteristics. In this research study the Active Yaw Control was optimized using the autonomous test mode and it enhances the driving behavior in a way that a 20% higher lateral acceleration can be reached. Under- or oversteering is avoided by different wheel torques on the rear axle without compromising longitudinal dynamics.

Keywords: Network analysis and control, Fault tolerant systems, System reconfiguration
Abstract: In this paper, we propose a method to establish a networked control system that maintains its stability in the presence of certain undesirable incidents on local controllers. We call such networked control systems weakly resilient. We first derive a necessary and sufficient condition for the weak resilience of networked systems. Networked systems do not generally satisfy this condition. Therefore, we provide a method for designing a compensator which ensures the weak resilience of the compensated system. Finally, we illustrate the efficiency of the proposed method by a power system example based on the IEEE 14-bus test system.

Keywords: Control over communication, Control over networks, Linear systems
Abstract: We propose a model-based event-triggered control scheme where state measurements are transmitted to the controller only if the deviation between the real system state and the state of a nominal closed-loop model crosses a certain threshold. In contrast to earlier results, the size of the thresholds is dynamically adapted to the unknown magnitude of the disturbances acting on the system. The closed-loop system is shown to be input-to-state stable. For a particular choice of the parameters, the guaranteed asymptotic bound on the system state is the same as for a periodically triggered scheme while still allowing a reduction in communication.

Keywords: Control over networks, Network analysis and control, Linear systems
Abstract: Stabilizability is a metric to measure the ability of a dynamical system to achieve asymptotic stabilization by feedback. Similar to this role, semistabilizability was originally proposed to measure the capability of a dynamical system to achieve semistable stabilization or equivalently, semistabilization by feedback. However, in this paper by conducting a further detailed discussion on the notion of semistabilizability, we find out its limitation and restriction to fully capture the semistabilization capability of linear systems. Thus, two new notions of strong semistabilizability and partial semistabilizability are proposed to fully characterize the semistabilization ability for linear systems. These notions are then used for semistabilization analysis of multi-layer networks formed by graph Cartesian products when each single layer of networks is semistabilizable.

Keywords: Decentralized control, Linear systems, Control over networks
Abstract: It has been shown in previous work that asynchronous event-triggered mechanisms can reduce measurement transmissions of control systems' implementations. In this paper we study the relation between minimum bandwidth of the feedback channels and the performance of linear systems. By using the S-procedure, the parameters in an asynchronous event-triggered implementation are optimized. Threshold update delays are considered, and two methods are presented to guarantee a certain performance under such delays. With the presented results, the implementations can be tuned to reduce the amount of communication rate while guaranteeing pre-specified performance levels. Simulation results are presented illustrating the applicability of this optimal asynchronous event-triggered implementation.

Keywords: Stochastic filtering, Communication networks, Optimization
Abstract: This study is concerned with an observer who desires to inform optimally a distant agent regarding a physical stochastic process in the environment. We consider that the observer has a constraint on the energy resource for the directed communication to the agent. The information we are interested in is the change in the knowledge possessed by the agent about the state of the process. We find the maximum information that can be transferred from the observer to the agent over a finite horizon subject to a bound on the total energy of the observer. We show that the maximum information is the optimal value of a mixed-integer nonlinear optimization problem. We obtain lower and upper bounds on the maximum information and also a suboptimal admissible solution based on a semi-definite programming. Moreover, we propose an optimized event-triggering mechanism based on a linear matrix inequality which yields event-driven sampling. Numerical and simulation results are presented for simple stable and unstable systems.

Keywords: Nonlinear system identification, Delay systems, Mechatronics
Abstract: The problem of forward and backward time delays is significantly important for both control and feedback loop of networked control systems. These time delays give rise to latency in performance and thereby may destabilize the system. Therefore numerous methods have been proposed about time delay identification/estimation and compensation for networked control systems, especially for bilateral teleoperation systems. However, most compensation methods have been accomplished by considering offline time delay estimation for linear/nonlinear time delay control systems.

In this work, we propose an observer based estimation algorithm for round trip delay which is the sum of forward and backward time delays for a 1 degree-of-freedom nonlinear bilateral teleoperation system. Via Lyapunov based stability analysis, global boundedness of the observer errors along with their ultimate convergence and the convergence of the round trip delay estimator to the vicinity of its real value can be guaranteed in the closed–loop system. Finally, simulation and experimental studies are carried out utilizing the last link of a PHANToM Omni Haptic device moving like a one–link robot in the vertical plane.

Keywords: Large-scale systems, Predictive control for nonlinear systems, Process control
Abstract: In this paper, Economic Model Predictive Control (EMPC) with periodic terminal constraints has been addressed for nonlinear differential-algebraic equation systems with application to Drinking Water Networks (DWNs). DWNs have some periodic behaviours because of the daily seasonality of water demands and electrical energy price. The periodic terminal constraint and economic terminal cost have been implemented in the EMPC controller design for the purpose of achieving the convergence. In terms of the stochastic system including the system disturbances, the feasibility of the proposed EMPC strategy has been guaranteed by means of the soft constraint instead of a hard constraint by means of adding a slack variable. Finally, the comparison results in the case study of the DTown water network has been shown when applying the EMPC strategy with or without periodic terminal constraints.

Keywords: Chemical process control, Optimization, Complex systems
Abstract: A study of the optimal real-time management of hydrogen H2 networks in oil refineries has been carried out. The paper addresses the main problems related to the operation of the networks combining data reconciliation with a real-time optimization RTO system for the optimal production and redistribution of hydrogen. Coherent and robust results have been achieved regarding the data reconciliation stage despite all the uncertainty in measurements and process operation, according to the off-line validation performed. Once the network state has been estimated, a RTO approach was followed aiming at the real-time optimal operation of the global refinery H2 network; an analysis of the solutions achieved was also performed. A predictive controller already commissioned and in operation is introduced; it is complementary to the RTO approach with the purpose of the on-line implementation of the hydrogen management optimal policies.

Keywords: Optimization, Reduced order modeling, Model validation
Abstract: The optimization of the operation of chemical plants may require the development of mathematical models of the process units of a plant. These mathematical models can be either first-principles or data-driven models. The former type of modeling may be complex for the use in optimization and especially for online applications such as real time optimization. Available measured process data can be used to develop the latter type of modeling. Although data-driven models offer several benefits for online applications, there are some very significant challenges related to their development in a practical industrial implementation. This paper discusses the important aspects of the building of data-driven models and demonstrates the effects of these types of models on the optimization results. The current work demonstrates the application of a real time optimization framework applied to an industrial air compressor station of an air separation plant when the models are based on operating data.

Keywords: Optimal control, Energy systems, Electrical power systems
Abstract: Increasing share of renewable power generation requires higher flexibility on electricity markets. Holistic energy management schemes for public, commercial and industrial sites and buildings offer potential to profit from those changes. In this paper we present several approaches of energy optimization for industrial and commercial sites as well as utilities that have been proven beneficial for site owners and users. The paper outlines a unique model-based optimizing control concept for distributed resources integrating multiple forms of energy.

Keywords: Process control, Optimal control, Predictive control for linear systems
Abstract: In this paper, we present our first results from an industrial application of model predictive control (MPC) with real-time steady-state target optimization (RTO) for control of an industrial spray dryer that produces enriched milk powder. The MPC algorithm is based on a continuous-time transfer function model identified from data and states estimated by a time-varying Kalman filter. The RTO layer utilizes the same linear model and a nonlinear economic objective function for calculation of the economically optimized targets. We demonstrate, by industrial application of the MPC, that this method provides significantly better control of the residual moisture content, increases the throughput and decreases the energy consumption compared to conventional PI-control. The MPC operates the spray dryer closer to the residual moisture constraint of the powder product. Thus, the same amount of feed produces more powder product by increasing the average water content. The value of this is 186,000 euro/year. In addition, the energy savings account to 6,900 euro/year.

Keywords: Distributed cooperative control over networks, Chemical process control, Optimization algorithms
Abstract: Site-wide resource allocation among different partially autonomous production plants in the process industries can be realized by price-based coordination. The individual production plants pursue their own objectives and only report the amount of shared resources that they want to produce or consume as a response to the price signals. In an iterative procedure, known as tâtonnement process, a central coordinator adjusts the transfer prices until an equilibrium price is achieved that balances the shared resource networks [1]. One of the drawbacks of the price-based coordination is the slow convergence of the tâtonnement process, which is very sensitive to the step size in the price update. In this contribution we propose a new price-update step that relies on a quadratic approximation of the network residual. For an academic example and an industrial case study of an integrated petrochemical site, simulation results are provided that show the improved convergence rate of the proposed technique.

[1] H. Uzawa, “Walras’ Theory in Tâtonnement of the Exchange,” Rev. Econ. Stud., vol. 27, no. 3, pp. 182–194, 2010.

Keywords: Iterative learning control, Automotive
Abstract: Control of Diesel Oxidation Catalyst (DOC) outlet temperature is critical for the downstream Diesel Particulate Filter (DPF) regeneration. However, the complexities of the reactions in DOC make it difficult to manage its outlet temperature due to model uncertainties including time delay mismatch. DPF regeneration is treated as a batch process and the Internal Model Control (IMC) based Iterative Learning Control (ILC) was used for DOC outlet temperature control in this paper. The IMC-based ILC consists of the standard IMC and historical data based ILC. The standard IMC is based on the process model with time delay identified from the high fidelity DOC model in GT-Power. The ILC is designed based on historical information including the controller input, plant output, and model predictive output stored in the ‘memory’. Simulation results through high-fidelity GT-Power model are compared with IMC alone method and show that IMC based ILC can have perfect tracking after several iterations.

Keywords: Iterative learning control, Identification, Nonlinear system identification
Abstract: In this paper we introduce a bilinear repetitive process and present an iterative subspace algorithm for its identification. The advantage of the proposed approach is that it overcomes the ``curse of dimensionality'', a hurdle commonly encountered with classical bilinear subspace identification algorithms. Simulation results show that the algorithm converges quickly and provides new alternatives for modeling/identifying nonlinear repetitive processes.

Keywords: Nonlinear system identification, Machine learning
Abstract: In this paper a new system identification approach for Hammerstein systems is proposed. A straightforward estimation of the nonlinear block through the use of LS-SVM is done by making use of the behavior of Hammerstein systems in steady state. Using the estimated nonlinear block, the intermediate variable is calculated. Using the latter and the known output, the linear block can be estimated. The results indicate that the method can effectively identify Hammerstein systems also in the presence of a considerable amount of noise. The well-known capabilities of LS-SVM for the representation of nonlinear functions play an important role in the generalization capabilities of the method allowing to work with a wide range of model classes. The proposed method’s main strength lies precisely in the identification of the nonlinear block of the Hammerstein system. The relevance of these findings resides in the fact that a very good estimation of the inner workings of a Hammerstein system can be achieved.

Keywords: Nonlinear system identification, Model validation, Biological systems
Abstract: The modeling and prediction of the methane production with anaerobic digestion processes is a complex task. Usually, first principles nonlinear models are used to fulfill this objective. These model structures are normally quite complex and some of the parameters may not be identifiable depending on the available measurement data. To overcome this problem, it is proposed the use of NAR and NARMA black-box models for modeling and prediction of methane production in batch bioreactors. First, simulations comparing well established nonlinear models with NAR and NARMA are proceeded and the selection of model regressors are based on the identified parameter values and the output relative errors. The domain of validity of the model and its parameters are analyzed for different concentrations of process initial conditions. To complete the validation experimental data are used to show the promising results in use these models for prediction of methane production in anaerobic batch bioreactors.

Keywords: Nonlinear system identification, Identification for hybrid systems, Adaptive systems
Abstract: In the paper, we investigate the identification of continuous piecewise affine systems in state space form with jointly unknown partition and subsystem matrices. The partition of the system is generated by the so-called centers. By representing continuous piecewise affine systems in the max-form and using a recursive Gauss-Newton algorithm for a suitable cost function, we derive adaptive laws to online estimate parameters including both subsystem matrices and centers. The effectiveness of the proposed approach is demonstrated with a numerical example.

Keywords: Nonlinear system identification
Abstract: Human-computer interactions are greatly affected by the latency between the human input and the system visual response. The compensation of this latency is an important problem for the HCI (human-computer interaction) community. In this work, a simple forecasting algorithm is developed for latency compensation in indirect interaction using a mouse, based on numerical differentiation. Several differentiators are compared, including a novel algebraic version. An optimized procedure is developed for tuning the parameters of the algorithm. The efficiency is demonstrated on real data, measured with a 1 ms sampling time.

Keywords: Behavioural systems, Optimal control, Linear systems
Abstract: We provide a complete set of necessary and sufficient conditions for both conservative (lossless) and passive single-input single-output systems (Theorems 5 and 7, respectively). These conditions generalise the famous lossless positive-real lemma and positive-real lemma, respectively, by extending them to include uncontrollable systems.

Keywords: Differential algebraic systems, Linear systems, Algebraic/geometric methods
Abstract: In this paper, we define the notion of bisimulation relations for DAE systems having a regular matrix pencil. It is well-known that under the assumption of regularity of the matrix pencil the state vector of the DAE system can be split into two parts: one corresponding to the "ordinary" input-state-output behavior corresponding to a standard proper transfer matrix, and the other one related to a polynomial transfer matrix. Employing the corresponding Wong sequences, we develop the notion of bisimulation relation between two regular matrix pencil DAE systems, being the direct product of two partial bisimulation relations corresponding to the fast and the slow subsystems.

Keywords: Emerging control theory, Fault tolerant systems, Uncertain systems
Abstract: In this paper, a Passive Fault Tolerant Control (PFTC) strategy for Linear Time Invariant (LTI) systems subject to actuator faults is proposed. The idea of this PFTC method is to compute a control law to cope with additive actuator faults using interval observers. The considered system is assumed to be subject to bounded noises and disturbances without any additional assumptions. The FTC is implemented as a state linear feedback control and designed using interval observers techniques. A numerical example shows the efficiency of the proposed technique.

Keywords: Fault detection and identification, Observers for linear systems, Linear systems
Abstract: This paper proposes a new Fault Tolerant Control technique based on the Multiple Models approach for linear systems with bounded perturbations and measurement noises. The consistency of each model with the measurements is checked at each sample time, using an ellipsoidal set-membership state estimation. A Min-Max Model Predictive Control is developed in order to find the optimal control and the best model in spite of the simultaneous presence of component and/or actuator and/or sensor faults. An illustrative example is analyzed in order to show the effectiveness of the proposed approach.

Keywords: Uncertain systems
Abstract: This papers presents the analysis and comparison of interval observer and set membership approaches for the state estimation of uncertain systems. The two approaches assume that noise and disturbances are unknown but bounded. In this paper, both approaches are compared when implemented using zonotopes. Mathematical expressions of both approaches are compared and conditions under which both approaches provide the same state estimation are derived. At the end, an example is used for showing the effect of these conditions on estimation.

Keywords: Computational methods, Optimal control, Behavioural systems
Abstract: Storage functions, which are also the Algebraic Riccati Inequality (ARI) solutions, play an important role in many optimal control/estimation problems. Extreme storage functions are solutions to the corresponding Algebraic Riccati Equation (ARE). While storage functions exist under assumption of dissipativity, a key assumption in formulation of the ARE/ARI is certain `regularity conditions' on the feedthrough term in the input/state/output representation of the system. For example, lossless and all-pass systems do not meet such regularity conditions (nonsingularity of D+D^T and I-D^TD respectively). And hence the ARE does not exist for such systems. Consequently, computation of storage functions for lossless/all-pass systems is not possible by conventional ARE based methods, and therefore, for such systems, different techniques are needed. In this paper we present three new algorithms for computation of storage functions for lossless/all-pass systems and compare them for numerical accuracy and computational efficiency. Each of the proposed methods presented in this paper comes from different viewpoints. One is linked to the notion of Bezoutian of two polynomials, while another is motivated by Foster realization of LC circuits and the third method is linked to the notion of trajectories of minimal dissipation in the behavioral approach. A comparative study among the three methods shows that the method based on the Bezoutian is the best from both perspectives: computational time and numerical accuracy.

Keywords: Algebraic Riccati Equation (ARE), Bezoutian, optimal control, Hamiltonian systems.

Keywords: Modeling, Identification
Abstract: For the day-ahead density forecasting of electricity load, this paper proposes the combination of the autoregressive moving average (ARMA) model and the generalized autoregressive conditional heteroskedasticity (GARCH) model, with both of them admitting exogenous inputs. This composite structure on the conditional mean and variance is referred to as the ARMAX-GARCHX model. As an alternative to its estimation by means of log-likelihood maximization, approaches based on iterative least-squares (ILS) and nonlinear least-squares (NLS) are considered. Apart from the ARMAX-GARCHX model, quantile regression models (QRMs) are also tested in forecasting where a wide range of quantiles are separately modeled to approximate a density. Phase currents of several low voltage transformer cables from the Netherlands are forecasted to compare the performances, and as the probabilistic evaluation criterion, the continuous ranked probability score is used. As an outline of the results, the ARMAX-GARCHX model outperformed QRMs and among its estimation techniques, the likelihood-based approach had the best performance, though the differences in the errors are often minor. Thus, owing to its computational simplicity, the ILS solution can be a valuable option when processing large batches of data in practice.

Keywords: Filtering, Signal processing, Aerospace
Abstract: This paper presents a variable-stepsize implementation of the unscented Kalman filtering for treating continuous-time stochastic models in radar tracking, numerically. Our method is grounded in the Gauss-type nested implicit Runge-Kutta formula of order~6 applied for solving moment differential equations (MDEs). The global error control implemented in this filter ensures that the MDEs are integrated numerically with negligible errors. The latter raises the accuracy of state estimation and makes our state estimator competitive to the accurate continuous-discrete extended Kalman filter (ACD-EKF) and the mixed-type accurate continuous-discrete extended-unscented Kalman filter (ACD-EUKF) developed earlier for target tracking models. The effectiveness of this new accurate continuous-discrete unscented Kalman filter (ACD-UKF) and its comparison to the ACD-EKF and ACD-EUKF methods are studied on a 7-dimensional radar tracking problem with both short and long waiting times. Our research suggests that the unscented Kalman filtering is more robust to the error accumulation and better suits for treating target tracking models with long sampling periods whereas the extended Kalman filtering is more accurate when the waiting time is short.

Keywords: Observers for nonlinear systems, Adaptive systems, Filtering
Abstract: This paper discusses the subject of unmeasurable parameter (or state) estimation. It presents a viable option for carrying out this task, as well as augmentations for mending its flaws. The selected basic method is Multiple Model Adaptive Estimation, using multiple Kalman Filters (KFs) in parallel to determine the current value of the parameter (or state) using other sensor measurements. However, this method is proven to give a staircase function as estimate in case of continuous variation of the unknown parameter. In some cases this leads to unacceptable estimation errors. One possible solution is to increase the number of KFs but this can also highly increase the computational load. Searching for alternative solutions resulted in the idea of using parabolic curve fitting on the discrete parameter values, so that the minimal value of the parabola could interpolate between the fixed values and so better locate the true parameter. Tests in an example showed that this method gives satisfactory results inside the covered parameter range but on the boundaries it can be inaccurate. With supplementation of the original parameter range (extension of the boundaries) and extrapolation of the parabolic curve one can finally achieve a highly accurate parameter estimate. This is demonstrated by an application example which offers calibrated airspeed estimation on a high-fidelity Airbus civil aircraft model.

Keywords: Observers for nonlinear systems, Biological systems, Lyapunov methods
Abstract: The problem of estimation of sequestered parasites Plasmodium falciparum in malaria, based on measurements of circulating parasites, is addressed. It is assumed that all (death, transition, recruitment and infection) rates in the model of a patient are uncertain (just intervals of admissible values are given) and the measurements are subject to a bounded noise, then an interval observer is designed. Stability of the observer can be verified by a solution of LMI. The efficiency of the observer is demonstrated in simulation.

Keywords: Observers for nonlinear systems, Lyapunov methods, Autonomous robots
Abstract: This paper considers a method of designing functional observers for continuous time nonlinear systems subject to unknown inputs. The proposed approach consists in rewriting the nonlinear model in a polytopic form (also known as multiple or Takagi-Sugeno models) applying the Sector Nonlinearity Transformation (SNT) and then apply the proposed algorithm for the observer design. Sufficient conditions for the asymptotic stability of the estimation error are given in terms of linear matrix inequalities (LMIs) and rank conditions. An application to a quadrotor aerial robots landing is then presented.

Keywords: Observers for nonlinear systems
Abstract: In this paper, a problem of persistent input design for the application of a Kalman-like observer to a class of systems which are not uniformly observable is considered. The class of systems is that of state-affine ones, for which Kalman filtering theory can be applied as soon as the input is defined as a function of time. In fact, it is first highlighted how an appropriate choice of the system input can improve the performance of the Kalman filter in this case. It is then emphasized how this input selection amounts to a control problem, which can be solved by an appropriate optimization approach. This input design is finally illustrated with some simulation results on an application example.

Keywords: Energy systems, Supervisory control, Hybrid systems
Abstract: Heating, ventilation, and air conditioning (HVAC) systems contribute significantly to energy consumption in buildings, and are the target of an ongoing push towards energy efficiency, which reflects on new requirements for the configuration and operation of HVAC units. On-off actuators are being replaced by staged or modulated ones, and additional components are being added to the HVAC units, which have to be properly managed by new, advanced control architectures. As such, it is increasingly more difficult for traditional control approaches to cope with new devices and meet new objectives. This leads to an opportunity for alternative, novel approaches to be adopted by the industry: promising are recently developed formal methods for controller synthesis. In this article, we employ formal, symbolic techniques to synthesize controllers for a model of a roof-top unit conditioning a low-rise commercial building. The synthesized controller is validated on a simulation with practically relevant operating conditions.

Keywords: Energy systems, Intelligent systems, Optimization
Abstract: This paper discusses the issue of demand side management, in particular control of the output power of heat pumps based on the spot market electricity price. The main presumptions are the ability of controlled HVAC system to shift energy load on the customer's side and sufficient credibility of an energy price prognosis on the electricity provider's side. The paper first presents current situation in the Czech republic with electricity tariffs legislations, which have to be followed so that the proposed method is applicable in practice. It is shown that for successful implementation, it is required to have an energy load model, model of the accumulation as well as parameters of the heat pump. For the energy load model, statistical black box methods are used, while the other models are based on first principles. The models are together with the prediction of spot market price used within model predictive control framework resulting in cost savings higher than 10%.

Keywords: Optimization, Energy systems
Abstract: The field of energy efficiency in buildings offers challenging opportunities from a control point of view. Heating, Ventilation and Air-Conditioning (HVAC) units in buildings must be accurately controlled so as to ensure the occupants’ comfort and reduced energy consumption. While the existing HVAC models consist of only one or a few HVAC components, this work involves the development of a complete HVAC model for one thermal zone. Also, a novel multivariable control strategy based on PI auto-tuning is proposed by combining the aforementioned model with optimization of the desired (timevarying) equilibria. One of the advantages of the proposed PI strategy is the use of time-varying input equilibria and zone set-point temperature, which can lead to important energy savings. A comparison with a baseline control strategy with constant set-point temperature is presented: the comparison results show good tracking performance and improved energy efficiency in terms of HVAC energy consumption.

Keywords: Energy systems, Model validation, Identification for control
Abstract: The research project (MPC-Boxes) deals with the design and construction of two test buildings (Test-Boxes), built for the purpose of performance evaluation of a model predictive controller (MPC) in comparison to a standard controller -- for heating and cooling via thermally activated building systems (TABS). The paper introduces the experimental environment, investigates the thermo-physical similarity of the two Test-Boxes, and deals with system identification related aspects. A simple third order state space model (SSM) is derived from first principles. This SSM served as a basis for the derivation of a structured SSM which is facilitated for parameter estimation by means of real measurement data. The performance of the structured SSM is validated with different identification data. The cross-validation performance decreases especially for longer validation intervals, however, within the MPC relevant prediction horizon the performance is still acceptable.

Keywords: Machine learning, Energy systems, Identification for control
Abstract: This paper presents an online transfer learning framework for improving temperature predictions in residential buildings. In transfer learning, prediction models trained under a set of available data from a target domain (e.g., house with limited data) can be improved through the use of data generated from similar source domains (e.g., houses with rich data). Given also the need for prediction models that can be trained online (e.g., as part of a model-predictive-control implementation), this paper introduces the generalized online transfer learning algorithm (GOTL). It employs a weighted combination of the available predictors (i.e., the target and source predictors) and guarantees convergence to the best weighted predictor. We further validate our results through experiments in climate control for residential buildings.

Keywords: Statistical learning, Fault detection and identification
Abstract: Heating, ventilation and air conditioning (HVAC) systems in buildings are subject to increasing expectations on performance. As such, HVAC systems need to be continuously monitored in order to early detect any anomalies which would degrade their performance. The building automation domain is subject to constraints which translate into the need for computationally efficient self-learning techniques. This paper provides an industrial R&D perspective on the topic with a more detailed focus on a modified algorithm for adaptive quantile estimation, which can be applied in various analytical workflows. This is shown on the examples of control performance monitoring and equipment fault detection. Real world results for control performance monitoring are presented and analyzed in more detail.

Keywords: Energy systems, Uncertain systems, Robust control
Abstract: The focus of this paper is on modeling and control of Smart Thermal Grids (STGs) in which the uncertainties in the demand and/or supply are included. We solve the corresponding robust model predictive control (MPC) optimization problem using mixed-integer-linear programming techniques to provide a day-ahead prediction for the heat production in the grid. In an example, we compare the robust MPC approach with the robust optimal control approach, in which the day-ahead production plan is obtained by optimizing the objective function for entire day at once. There, we show that the robust MPC approach successfully keeps the supply-demand balance in the STG while satisfying the constraints of the production units in the presence of uncertainties in the heat demand. Moreover, we see that despite the longer computation time, the performance of the robust MPC controller is considerably better than the one of the robust optimal controller.

Keywords: Large-scale systems, Stochastic systems, Predictive control for linear systems
Abstract: This paper presents a stochastic model predictive control approach for a thermal grid with uncertainties in the consumer demand profiles. This approach leads to a finite-horizon chance-constrained mixed-integer linear optimization problem at each sampling time, which is in general non-convex and hard to solve. Earlier approaches for such problems are either suboptimal ad-hoc methodologies, or computationally intractable formulations. We provide a unified framework to deal with production planning problems for uncertain systems, while providing a-priori probabilistic certificates for the robustness properties of the resulting solutions. Our methodology is based on solving a random convex optimization problem to compute the uncertainty bounds using the so-called scenario approach and then, solving a robust mixed-integer optimization problem with the computed randomized uncertainty bounds at each sampling time. Using a tractable approximation of uncertainty bounds, the proposed problem formulation retains the complexity of the problem without chance constraints. In the presented thermal grid application this implies that a robust mixed-integer program is solved to provide a day-ahead prediction for the thermal energy production plan in the grid. The performance of the proposed methodology is illustrated using Monte Carlo simulations and employing two different problem formulations: optimization over input sequences (open-loop MPC) and optimization over affine feedback policies (closed-loop MPC).

Keywords: Predictive control for linear systems, Stochastic systems, Energy systems
Abstract: In order to cope with uncertainties present in the renewable energy generation, as well as in the demand consumer, we propose in this paper the formulation and comparison of three robust model predictive control techniques, i.e., multi-scenario, tree-based, and chance-constrained model predictive control, which are applied to a nonlinear plant-replacement model that corresponds to a real laboratory-scale plant located in the facilities of the University of Seville. Results show the effectiveness of these three techniques considering the stochastic nature, proper of these systems.

Keywords: Optimization algorithms, Optimization, Electrical power systems
Abstract: The large-scale integration of renewable energy sources, in particular wind and solar, poses many challenges to power grid operations due to their stochastic and highly-variable nature. One of such challenges is the high cost associated with making real-time power balancing adjustments in order to compensate for forecast errors in renewable powers. To overcome this challenge, stochastic optimization techniques have been explored in the literature for planning generator dispatches taking into account renewable energy uncertainty and balancing costs. The techniques used are typically based on forming Sample Average Approximations (SAA) and applying deterministic optimization techniques that exploit the problem structure. In this work, the performance of alternative algorithms based on Stochastic Approximation (SA) and hybrid techniques for solving the stochastic optimal dispatch problem is analyzed. More specifically, an approach based on updating the certainty-equivalent problem with noisy gradient observations is compared against the stochastic gradient and two SAA-based algorithms on four test cases. This approach is shown to be equivalent to a stochastic proximal gradient algorithm with a non-Euclidean metric when applied to the stochastic optimal dispatch problem. The results obtained show that the adaptive certainty-equivalent algorithm produces better iterates compared to the other algorithms on the test cases considered.

Keywords: Electrical power systems, Hybrid systems, Optimization
Abstract: Recently, the idea of using fuel cell vehicles as the future way of producing electricity has emerged. A fuel cell car has all the necessary devices on board to convert the chemical energy of hydrogen into electricity. This paper considers a scenario where a parking lot for fuel cell cars acts as a virtual power plant. In order to describe the system behavior from the energy point of view, a hybrid (mixed logical dynamical) model is constructed. With this model, a control system is designed to determine the production profile for both the fuel cell and battery of each car in the parking lot subject to minimizing the operational cost. In order to deal with both the uncertainty in the demand profile and the power balance constraint, a robust min-max model predictive control algorithm is developed. The effectiveness of the proposed approach is illustrated in a numerical example.

Keywords: Markov processes, Energy systems
Abstract: This paper proposes a novel sequential decisionmaking strategy for a demand response aggregator that participates in the day-ahead market and reacts to imbalance prices. Finding such a participation strategy requires solving a multistage optimization problem under uncertainty that entails both an open-loop (day-ahead market) and a nested closed-loop (imbalance system) problem. Driven by the possibility of using data-driven models and reinforcement learning techniques, we formulate the problem as a Markov Decision Process (MDP). Standard MDP-based methods, however, often suffer from the curse of dimensionality. To address this challenge, we use techniques from approximate dynamic programming. Our proposed method applies a cross-entropy method with a simulation-based approximate policy iteration algorithm nested inside. The cross-entropy method is compared with a separated planning method, that optimizes the day-ahead and real-time decisions separately. The paper presents an empirical evaluation of the presented method for an aggregator with a fleet of electric vehicles using data from the Belgian electricity market. Moreover, it is assumed that the aggregator is a price taker in both the dayahead and real-time market.

Keywords: Automotive, Modeling, H2/H-infinity methods
Abstract: In automotive application field, reducing electric conductors dimensions is significant to decrease the embedded mass and the manufacturing costs. It is thus essential to develop tools to optimize the wire diameter according to thermal constraints and protection algorithms to maintain a high level of safety. In order to develop such tools and algorithms, accurate electro-thermal models of electric wires are required. However, thermal equation solutions lead to implicit fractional transfer functions involving an exponential that cannot be embedded in a car calculator. This paper thus proposes an integer order approximation methodology based on a spatial discretization for this class of fractional transfer functions. Moreover, the H2-norm is used to minimize approximation error. Accuracy of the proposed approach is confirmed with measured data on a 1.5 mm2 wire implemented in a dedicated test bench.

Keywords: Automotive, Observers for nonlinear systems, Stochastic filtering
Abstract: Selective catalytic reduction (SCR) continues to be the preferred technology for abatement of oxides of nitrogen (NOx) from diesel engines, yet challenges remain to bring SCR efficiency up to the level required by legislation. Such efficiency gains are predicated on improved control, which in turn relies in part upon improved state estimation, due to suboptimal plant observability. SCR relies on the injection of urea solution to convert harmful NOx to nitrogen and water, whilst avoiding excess ammonia leaving the tailpipe. Ammonia sensors to detect such events are costly and not yet production ready. Knowledge of the quantity of ammonia stored in the catalyst is necessary for control, but this cannot be measured directly. Finally, NOx sensors are cross sensitive to ammonia by an unknown nonlinear function of temperature. We design a high accuracy state estimator in the form of a particle filter to estimate these quantities. Furthermore, we demonstrate a fast implementation of this estimator using a graphics processing unit (GPU) to demonstrate the real time accuracy possible with modern computing platforms.

Keywords: Automotive
Abstract: This paper presents an improved scheme of fractional PID controller applied to the torque control problem of spark ignition (SI) engines. The objectives are to produce a minimum torque tracking error while obtaining fewer fuel consumption during the process of combustion. This is then resulted to provide a fast and monotonic air flow response into the engine cylinders by adjusting the throttle and EGR valve and the cam timing. This consideration also pushes the engine to work in its safe operational condition, avoiding from both knocking and misfiring damage. Afterwards, a preliminary investigation to obtain maximum efficiency is conducted on the idea of exploiting Genetic Algorithm that is commonly used in parallel optimization of controller coefficients. Eventually, simulation results illustrate effectiveness of proposed scheme in comparison with classical PID controller method.

Keywords: Automotive, Adaptive systems, Adaptive control
Abstract: The problem of air-fuel ratio (AFR) stabilization at the stoichiometric level is addressed in the paper. Two solutions of this problem based on the inverse dynamics principle are proposed. The first one consists in building empirical model of the engine, its on-line identification and further inversion. The second approach assumes building inverse model of the engine initially and then its identification. The both models – direct and inverse – are presented by grey boxes with physically-inspired input functions and structures. The models are used for the derivation of two feedforward controls with the parameters tuned online. The feedforwards with the estimated parameters provide the compensation of plant uncertainties, nonlinear dynamics and the delay of AFR measurement.

Keywords: Identification, Automotive
Abstract: In this paper, a mapping calibration method based on D-optimization algorithm is proposed and applied to the air mass calibration problem. The first procedure is to carry out a preliminary experiment around the main operating domain, and the polynomial regression model is chosen by minimum cAIC criteria. The second procedure is to calculate D-optimal design of experiment for the given model. The experiment results on a full-scale engine test bench is demonstrated to confirm that the proposed method can provide the precise model.

Keywords: Optimization algorithms, Stochastic control, Statistical learning
Abstract: In internal combustion engines, one of the most important factors influencing performance is the combustion phase, which is represented by the crank angle of 50% burnt (CA50) in this paper. In order to optimize the performance, which is represented by the indicated mean effective pressure (IMEP), CA50 should be controlled to track its optimal reference. IMEP can be considered as a function of CA50 coupled with stochastic noise, and thus leads to a stochastic optimization problem. A gradient based stochastic approximation algorithm is adopted to solve this problem. To estimate the gradient, a sample based probabilistic gradient approximation approach is developed, in which the probabilistic guarantee of estimation accuracy can be attained by adjusting the number of samples adaptively. Finally, the experimental validation is conducted on a SI gasoline engine test bench.

Keywords: Process control, Optimization, Maritime
Abstract: Iceberg drift forecast is a challenging process. Large uncertainties in iceberg geometry and driving forces prevent accurate forecasts. In this work, a moving horizon estimation approach that uses past drift information of the iceberg to correct the uncertainties is proposed to improve the forecast. Simple criteria are introduced to aid the decision of which uncertain parameters are most beneficial to estimate. In addition, it is discussed why other choices result in a lower prediction performance after the estimation process. Based on these considerations, the moving horizon estimator is implemented on a drift trajectory of an iceberg surveyed during a research expedition Offshore Newfoundland in 2015. It is demonstrated that the iceberg drift forecast improves significantly within a short-time frame. Furthermore, it is shown that the approach will in general also improve 24 hour iceberg drift predictions.

Keywords: Maritime, Robust control, Autonomous systems
Abstract: This paper proposes a novel cost-effective robust Model Predictive Control (RMPC) approach that can handle stochastic uncertainties with infinite support. The robust controller is developed by explicitly considering system and uncertainty properties and is applied to waterborne AGVs against environmental disturbances due to wind, waves, and currents. Specifically, probabilistic distributions are modeled and integrated in tube-based RMPC with optimized uncertainty bounds. Furthermore, successive linearizations of nonlinear system dynamics and non-convex constraints are implemented for ease of computational complexity and the robust design. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

Keywords: Maritime
Abstract: Heading and speed control for a patrol vessel is addressed by using simple PID regulators provided with an anti-windup setup. We rely on a decoupled linearized model of the original motion equations to design the proposed regulators. Specifically, the selection of the PID and anti-windup parameters is accomplished by using LMIs. The effectiveness of the resulting controllers is validated by means of simulations on the original, nonlinear dynamic equations and in the presence of external disturbances such as wind, waves, and current.

Keywords: Modeling, Maritime, Robotics
Abstract: This study examines the simulated effects of wind on the spatial surface distribution of pelletized feed from rotary pneumatic spreaders which are used extensively in sea cage aquaculture. A robotic model of the spreader and external ballistic description of the pellet trajectories have been extended to include wind forces, and the spatial distribution is compared for different sized pellets in various wind fields. The results show that overall effects of wind on spatial pellet distribution is limited, however, there is a negative correlation between wind and surface coverage.

Keywords: Optimization, UAV's, Maritime
Abstract: In this paper we propose a novel numerical approach to the design of smooth trajectories for fixed-wing Unmanned Aerial Vehicles (UAVs) with applications to target tracking of marine vehicles. Given a desired geometric path with respect to a possible moving target vehicle, we are interested in computing a feasible UAV trajectory that best approximates in L2 sense the desired geometric moving path with a specified airspeed profile assigned on it. Due to communication range limitations (e.g., the UAV is operating as a wireless communication relay between a target vehicle and a ground station), the UAV trajectory needs to satisfy given path constraints. Space-varying wind is also taken into account. We address this problem by taking a Virtual Target Vehicle (VTV) perspective. We set up a suitable optimal control problem based on the error coordinates between the UAV and the VTV. We solve the optimal control problem numerically by using PRONTO, a very versatile control optimization tool enabling to deal with a wide variety of trajectory functionals and constraints. We provide and discuss numerical computations based on a practical scenario where an Autonomous Surface Vehicle (the target vehicle) transmits data to the UAV which sends them back to a ground station.

Keywords: Robotics, Sliding mode control, Nonlinear system theory
Abstract: Intervention on underwater structures using an ROV/manipulator system is common practice in the oil and gas industry. This paper presents a novel control scheme enabling the end-effector to keep the desired set point in unknown, time-varying current. This is crucial for safe and reliable intervention. A kinematic control scheme is suggested, where the tracking error is taken into account in generating reference velocities. The proposed scheme is compared to two other approaches, one reducing the problem to end-effector stabilization with a base with unknown motion and one using full regular kinematic control. Simulations suggest that full regular kinematic control performs worst due to the difficulty of following ROV body reference velocities. Reducing the problem to end-effector stabilization with unknown base motion yields somewhat better accuracy, whereas the suggested scheme employing knowledge about the velocity tracking error increases accuracy significantly.

Keywords: Predictive control for linear systems, Process control
Abstract: When a model based control solution is to replace an existing simpler solution, you will want the previous solution to stay available for use in production, until the replacement is completely commissioned. The paper presents a method to make a Model Predictive Controller (MPC) replicate the behavior of an existing solution involving a number of PI controllers. Thereby it can replace the existing solution already before you have a reliable model to use in it. It is first shown how to get exactly the same feedback control in a SISO MPC as with an existing PI controller. The extension to several PI controllers, in combination with other elements like minimum and maximum selectors, is exemplified by some cases with two PI controllers: override control, cascade control, mid-ranging control and ratio control.

Keywords: Predictive control for linear systems, Robust control, Switched systems
Abstract: This paper proposes an approach to robust model predictive control (MPC) for discrete-time jump Markov linear systems (JMLS) considering polytopic constraints on the inputs and states. In a first design step, state feedback controllers, that stabilize the JMLS robustly, are calculated offline by means of a semi-definite program (SDP). These controllers are designed to satisfy the constraints and keep the states within disturbance invariant sets (DIS). To reduce the conservatism of the design approach, an SDP formulation in which the controller parameterization is independent of the Lyapunov matrices is employed. The resulting Lyapunov matrices and the DIS are used to formulate quadratic constraints for the first prediction step, that ensure robustness against additive disturbances, stability, constraint satisfaction and recursive feasibility. The stabilizing properties and low computation times of the resulting quadratically constraint quadratic program (QCQP) are illustrated by simulation.

Keywords: Predictive control for linear systems, Stochastic control
Abstract: This paper presents the design of the Unrestricted Horizon Predictive Controller, short UHPC, evaluated from the extended horizon of a minimal order Generalized Minimum Variance controller investigated in a free Diophantine equation form based on ARMAX models. In contrast to common MPC methods, UHPC does not employ the receding horizon approach for calculation of its future control steps, but a state space solution where a 1-step ahead Kalman Filter and the inherent calculation of two Diophantine equations – one for the control signal and other for the noise – are utilized. Simulation results show that UHPC performs well compared to the most common approaches (Minimum Variance and Generalized Predictive Control) for several different plant conditions, such as regulation (noise rejection) and reference tracking.

Keywords: Predictive control for linear systems, Computer aided control design
Abstract: The paper shows how explicit representations of model predictive control (MPC) feedback laws can be embedded into Python applications via a new code-generation module of the Multi-Parametric Toolbox. The advantage of the explicit approach is that it provides a simple and fast computation of optimal control inputs without solving optimization problems on-line. To enable implementation of discontinuous feedback laws, the paper proposes an extended version of the sequential search algorithm which resolves possible multiplicities based on a secondary evaluation of the cost function. Two applications are considered. The first one is the Flappy Bird game where we design an MPC-based artificial player to control flapping of the bird's wings. The second application considers the design and implementation of an explicit MPC controller for a quadrocopter.

Keywords: Predictive control for linear systems, Optimal control, Mechatronics
Abstract: The development of efficient solution approaches and technological advances facilitate the use of predictive control on embedded systems, even for fast systems or on computationally limited hardware platforms. The practical implementation of predictive control is, however, still often very time consuming and demands insight into the formulation and solution strategies for predictive control. Tools for automatic code generation tailored for deployment on embedded systems promise to overcome these problems and thus enable the fast and reliable implementation of predictive control. This paper exploits the efficiency and performance of automatic code generation for linear model predictive control for the embedded active vibration control of a flexible mechanical structure. muAO-MPC is used to automatically generate C code, based on a high level problem description. The resulting code is used for real-time implementation on an embedded platform. The embedded model predictive controller efficiently computes the voltage input for a piezoceramic actuator based on state estimates from a Kalman filter. The performance, computational efficiency, memory requirements, task execution timing and other properties of practical interest are examined via experiments on the embedded controller for active vibration control.

Keywords: Predictive control for linear systems, Optimization algorithms
Abstract: This paper tackles some important issues in the use of target information by model predictive control (MPC) that have largely been ignored in the literature. First the paper shows explicitly how far future information of target changes affects an optimal predictive control (OMPC) for both the unconstrained and constrained case. Secondly, the paper develops on proposal in the literature which deals with scenarios where the desired target is unreachable due to constraints. Numerical illustrations in MATLAB give evidence of the efficacy of the proposals.

Keywords: Identification, Filtering
Abstract: In this work an interval observer is proposed for on-line estimation of differentiation errors in some class of high-order differentiators (like a high-gain differentiator from [#Vasiljevic2008], or homogeneous nonlinear differentiator from [#Perruquetti2008], or super-twisting differentiator [#Levant1998]). The results are verified and validated on the telescopic link of a robotic arm for forestry applications in which the mentioned approaches are used to estimate the extension velocity while the interval observer gives bounds to this estimation.

Keywords: Identification, Quantized systems
Abstract: The work presented in this paper focuses on the recursive identification of finite impulse response (FIR) systems with binary valued measurements. The main difficulty with such an identification is the low resolution of the available data on the output. It is first shown that this low resolution can be sufficient for the identification of the system. Then, the identification problem is formally posed as a bounded error identification problem, this allows the use of a simple recursive algorithm. Performance of the proposed algorithm are analyzed. Finally, simulation results are given to demonstrate the efficiency of the method.

Keywords: Identification, Statistical learning
Abstract: We consider an on-line system identification setting, in which new data become available at given time steps. In order to meet real-time estimation requirements, we propose a tailored Bayesian system identification procedure, in which the hyper-parameters are still updated through Marginal Likelihood maximization, but after only one iteration of a suitable iterative optimization algorithm. Both gradient methods and the EM algorithm are considered for the Marginal Likelihood optimization. We compare this ``1-step'' procedure with the standard one, in which the optimization method is run until convergence to a local minimum. The experiments we perform confirm the effectiveness of the approach we propose.

Keywords: Identification, Statistical learning
Abstract: This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm. Results regarding point estimators for the impulse response as well as for confidence regions are reported.

Keywords: Identification
Abstract: An errors-in-variables problem where the system as well as the white measurement noises are in continuous-time is considered. Due to the intrinsic nature of the measurement noises, a strategy of lowpass filtering followed by instantaneous sampling is used for obtaining data from the system. A previously developed covariance function based parameter estimation method is first slightly improved. Thereafter, it is analyzed by evaluating the covariance matrix of the estimated parameter vector. Three different expressions for a generic element of an intermediate matrix in the expression for the covariance matrix are derived. One exact but computationally demanding, one approximate valid for small sampling intervals, and one exact for the case when the sampling interval tends to zero. The covariance matrix can be used for studying the influence of some user parameters, including the choice of the lowpass filter, on the quality of the estimated parameter vector.

Keywords: Identification, LMI's/BMI's/SOS's, Uncertain systems
Abstract: We propose a subspace identification method that involves a priori information of the system characterized in the frequency domain. Some properties of the system over all frequency range are transformed into matrix inequalities that are linear in system matrices, by using the well-known Kalman-Yakubovich-Popov (KYP) lemma. To construct a model that represents the specified frequency characteristics, we formulate a subspace identification problem under the matrix inequality constraints. This constrained problem is in a class of nonlinear optimization problems, then we reduce it to a convex one by applying a proper transformation. Furthermore, the proposed method is extended to that incorporated with a priori information characterized only in a certain frequency range. Finally, we verify the effectiveness of the proposed method in a numerical simulation.

Keywords: Linear systems, Optimal control
Abstract: This paper introduces a new decomposition of the constrained generalized discrete-time algebraic Riccati equation arising in linear quadratic optimal control problems into two parts: the first part is an explicit expression which is common to all solutions. The second part can be either a reduced-order discrete-time algebraic Riccati equation with non-singular associated closed-loop matrix, or a symmetric Stein equation.

Keywords: Linear systems, Stability of linear systems, Robust control
Abstract: In order to understand the governing principles of a specific topic, e.g., control design, and to be able to design efficient algorithms a sound mathematical framework is needed. Due to the complexity of the problems, however, there are different mathematical tools that fit to our needs and which highlights specifics aspects of a given field.

In the recent research of the authors concerning global geometrical aspects of robust control theory it turns out that the proper mathematical language for the considerations seems to be a Jordan algebraic one, more precisely the framework of the Jordan pairs that is closely related to geometric, generalised projective geometric ideas. Moreover, this mathematical framework is closely related to the theory of unbounded and bounded symmetrical domains, where we can rediscover the concept of quadratic invariance, an efficient tool for the design of decentralized control systems.

Since these mathematical tools seem to be completely unused in the previous control theoretical researches, in this paper we try to give a glimpse on the field. Our aim is to point out the main connections of this mathematical framework and control theory and to illustrate the potential of the framework for control problems.

Keywords: Linear systems, Stability of linear systems
Abstract: This paper is concerned with the problem of computing basis matrices for the fundamental output-nulling subspaces and the simultaneous computation of the associated friends that place the assignable closed-loop eigenvalues at desired locations. In particular, our aim is to show that the Moore-Laub algorithm for the computation of these subspaces was stated under unnecessary restrictive assumptions.

Keywords: Linear systems
Abstract: We consider the classic problem of row-by-row input-output decoupling by state feedback. We utilise the methods of a recent work by two of the present authors to offer a new design method to obtain a feedback matrix that will solve the decoupling problem and also assign a desired set of closed-loop poles.

Keywords: Linear time-varying systems, Observers for linear systems, Stability of linear systems
Abstract: In this paper and the companion work [9], we deal with linear systems and investigate the concepts of stabilizability and detectability in the finite-time context. Here, our aim is to study the relashionships between the existence of observer based output feedback finite-time stabilizing controllers and the concepts of finite-time stabilizability (FT-stab) and detectability (FT-det). In the classical Lyapunov context, the Separation Principle states that stabilizability and detectability of the given linear system are necessary and sufficient for the existence of an output feedback dynamical controller which, without loss of generality, can be given a controller-observer structure. We show that this is no longer true in the finite-time context; therefore, we provide a further sufficient condition for the existence of an observer-based output feedback controller which finite-time stabilizes the closed loop system. Based on this result, a procedure for the design of a suitable controller is provided; such procedure requires the solution of some optimization problems constrained by DLMIs. A numerical example illustrates the benefits of the proposed approach.

Keywords: Linear time-varying systems, Stability of linear systems, LMI's/BMI's/SOS's
Abstract: In this paper, the first of two companion works, we deal with linear systems and extend to the finite-time setting the concepts of stabilizability and detectability. After stating necessary and sufficient conditions for finite-time stabilizability (FT-stab) and detectability (FT-det), in terms of feasibility conditions constrained by differential linear matrix inequalities (DLMIs), we investigate the relationships between the existence of dynamical output feedback finite-time stabilizing controllers and the concepts of FT-stab and FT-det. In the classical Lyapunov framework, a consequence of the well known Separation Principle is that stabilizability via dynamic output feedback controllers is equivalent to stabilizability (via state feedback) plus detectablity. In this paper, we show that, even in the finite-time context, stabilizability and detectability play a role into the existence of stabilizing dynamical controllers, although with some differences. Indeed we prove that a dynamic output feedback controller which finite-time stabilizes the overall closed loop system exists if and only if the open loop system is finite-time detectable and stabilizable plus a further LMI condition. Based on this result, a procedure for the design of a suitable output feedback controller is provided; such procedure requires the solution of some optimization problems constrained by DLMIs. A numerical example illustrates the benefits of the proposed approach.

Keywords: Observers for nonlinear systems, Lyapunov methods
Abstract: For a family of continuous-time nonlinear systems with input, output and disturbances in the case where measurements are available only at discrete instants, a new interval observer design is proposed. The family covers bilinear (and linear) systems with static output feedback as special cases. Employing the structure of Luenberger-type observers, we construct framers that allow us to determine a lower and an upper bounds of state variables in the presence of disturbances, provided that intervals in which uncertain initial conditions and uncertain disturbances lie are known. It is proved that the lower and upper bounds of state variables converge to each other completely when the maximum time interval of measurements is sufficiently small in the absence of disturbances.

Keywords: Observers for nonlinear systems
Abstract: In this note the low-power observer structure presented in [1] is modified to avoid peaking of the observer states while preserving its good sensitivity properties to measurement noise and the implementation advantages in terms of power-gain with respect to standard high-gain observers.

Keywords: Quantum control, Observers for linear systems, Quantum information and control
Abstract: This paper extends previous results on constructing a direct coupling quantum observer for a quantum harmonic oscillator system. In this case, we consider a complex linear quantum system plant consisting of a network of quantum harmonic oscillators. Conditions are given for which there exists a direct coupling observer which estimates a collection of variables in the quantum plant. It is shown that the order of the observer can be the same as the number of variables to be estimated when this number is even and thus this is a reduced order observer.

Keywords: Stochastic filtering, Stochastic systems, Observers for linear systems
Abstract: Only few estimation methods can converge in the presence of impulsive measurement and/or process noises without the use of augmented heuristic schemes. To understand the performance of these schemes, the optimal Idan/Speyer Cauchy Estimator (ISCE) is compared with the performance of the particle filter (PF) and Gaussian sum filter (GSF) as the convergence time of these estimators is allowed to increase. That is, the number of particles at each step for the PF and the number of Gaussian components at each step for the GSF are increased and their performance relative to the ISCE is numerically studied for scalar and two-state dynamic systems.

Keywords: Sensor and signal fusion, Filtering, Stochastic filtering
Abstract: This paper presents a Bayesian indoor positioning system for smartphones based on the strengths of WiFi and Bluetooth signals. A framework for improving the performance of existing positioning methods with the help information sharing between users is proposed and evaluated. Bluetooth signals are sent between users, and the signal strengths contain information about their relative distances, which is used to evaluate the probability distribution functions of their states. A particle filter is used for the state estimation, together with an unscented transform to propagate probability distributions through nonlinearities.

Keywords: Agents and autonomous systems, Concensus control and estimation, Control over networks
Abstract: We investigate the problem of social/opinion networks of autonomous agents, each of which has a personal view that follows an independent dynamic behavior and it communicates with their neighbors under a cooperative algorithm. We apply mathematics from non-negative matrix theory. We investigate agents with identical and non-identical views and we establish sufficient conditions for stability and convergence to a common synchronized opinion.

Keywords: Energy systems, Fault detection and identification, Robust adaptive control
Abstract: The problem of model-based icing detection for wind turbines is addressed in this paper. A robust observer of the rotor angular speed is designed in order to detect the increase of inertia and the change of aerodynamic torque. The amount of ice accretion is approximated through an online estimator. A suitable threshold based on the ice estimate and an associated logic are defined in order to stop the wind turbine when the icing appears to be too severe.

Keywords: Energy systems, Optimal control
Abstract: We consider the operation of a wind turbine with the goal of maximizing the total energy generated while respecting temporary boost commands for the power delivered to the grid and limits on the rotor speed and generator power preceding a boost. Power boosting capability is required of wind turbines in a number of grid codes in order to help stabilize the grid. We transform the problem to one with linear dynamics and convex constraints and implement the optimal control problem in a receding horizon manner. We demonstrate how an intuitive formulation can control the turbine during the boost and the subsequent recovery phase such that the kinetic energy stored in the wind turbine rotor is not to drained to a critical low level. We provide extensive closed-loop tests with an industrial wind turbine simulator.

Keywords: Energy systems, Predictive control for linear systems
Abstract: The use of upstream wind measurements has motivated the development of blade-pitch preview controllers to improve rotor speed tracking and structural load reduction beyond that achievable via conventional feedback design. Such preview controllers, typically based upon model predictive control (MPC) for its constraint handling properties, alter the closed-loop dynamics of the existing blade-pitch feedback control system. This can result in the robustness properties of the original closed-loop system being no longer preserved. As a consequence, the aim of this work is to formulate a MPC layer on top of a given output-feedback controller, with a view to retaining the closed-loop robustness and frequency-domain performance of the latter. The separate nature of the proposed controller structure enables clear and transparent qualifications of the benefits gained by using preview and predictive control. This is illustrated by results obtained from closed-loop simulations upon a high-fidelity turbine, showing the performance comparison between a nominal feedback compensator and the proposed MPC-based preview controller.

Keywords: Energy systems, Nonlinear system theory
Abstract: The continuous increase in the size of wind turbines (WTs) has led to new challenges in the design of novel torque and pitch controllers. Today’s WT control design must fulfill numerous specifications to assure effective electrical energy production and to hold the tower vibrations inside acceptable levels of operation. Hence, this paper presents modern torque and pitch control developments based on the super-twisting algorithm (STA) by using feedback of the foreaft and side-to-side acceleration signals of the WT tower. According to numerical experiments realized using FAST, these controllers mitigate vibrations in the tower without affecting the quality of electrical power production. Moreover, the proposed controllers’ performance is better than the baseline controllers used for comparison.

Keywords: LMI's/BMI's/SOS's, Uncertain systems, Modeling
Abstract: In this paper, two alternative Linear Matrix Inequality (LMI) approaches were used to derive a decentralised control for an innovative 5 MW wind turbine with a hydrostatic transmission. With LMIs, given parameter uncertainties can be considered adequately. The proposed control covers the whole range from low to very high wind speeds. An active damping of tower oscillations is achieved by using the pitch angle as control input. Moreover, a robust multi-variable drive train control is designed that allows for tracking of desired trajectories for the angular velocities of both the rotor and the generator. The overall control performance is illustrated by realistic simulation results, which show an improved damping of tower oscillations and an excellent tracking behaviour for the controlled variables despite parameter uncertainties.

Keywords: Mechatronics, Emerging control applications, Energy systems
Abstract: This paper presents a concept for hardware-in-the-loop (HiL) drive train control of a 10 MW full-scale ground test facility for wind energy converters(WEC). This is to enable realistic emulation of the missing rotor torque, in order to provide a realistic test environment under load conditions comparable to those in the field. The HiL framework consists of a dynamic rotor model coupled with the test rig drive train in a suitable structure. The goal is to apply a realistic torque on the main shaft of a device under test being comparable to that of an ideal WEC model. Therefore, accurate reproduction of the torque with respect to its dynamic and steady-state properties is required. Consequently, active vibration damping of the drive train is necessary due to the discrete mass structure of the drive train and finite elasticity of the intermediate couplings, and also enough degrees of freedom is required to influence frequency response of the closed-loop system in and around the torsional modes. Hence, the drive train has been modelled and an estimation-based torque control strategy has been proposed taking into account torsional behaviour of the drive train and the virtual rotor. In the proposed state-space control structure, a linear-quadratic-gaussian regulator and a constrained model predictive controller (MPC) explicitly considering the actuator's physical limitation have been implemented, while the unmeasured state-variables are to provided by a time-varying Kalman filter. For an evaluation of the proposed approach, simulation results are provided and compared. Additionally, interaction of the coupled dynamic subsystems is analysed and illustrative conclusions are made. Overall, the proposed HiL framework leads to an accurate rotor inertia emulation and enables reproduction of the virtual rotor's torsional mode.

Keywords: Electrical power systems, Energy systems
Abstract: We consider the problems of stability, frequency restoration and optimal steady-state resource allocation in a heterogeneous and structure-preserving differential-algebraic equation (DAE) power system model. Thereby, we include constant-power-controlled loads (CPCLs) and constant-power-controlled sources (CPCSs) explicitly in the analysis and network control design. This results in a power system model with mixed algebraic as well as first- and second-order differential dynamics. We show that the abovementioned control objectives can be achieved via a distributed averaging proportional integral (DAPI) control and, in particular, extend the stability proof in [1] to the resulting closed-loop DAE system.

Keywords: Decentralized control, Energy systems
Abstract: In this paper, we provide an extension of the scalable algorithm proposed in (Riverso et al., 2015) for the design of Plug-and-Play (PnP) controllers for AC Islanded microGrids (ImGs). The method in (Riverso et al., 2015) assumes DGUs are arranged in a load-connected topology, i.e. loads can appear only at the output terminals of inverters. For handling totally general interconnections of DGUs and loads, we describe an approach based on Kron Reduction (KR), a network reduction method giving an equivalent load-connected model of the original ImG. However, existing KR approaches can fail in preserving the structure of transfer functions representing transmission lines. To avoid this drawback, we introduce an approximate KR algorithm, still capable to represent exactly the asymptotic periodic behaviour of electric signals even if they are unbalanced. Our results are backed up with simulations illustrating features of the new KR approach as well as its use for designing PnP controllers in a 21-bus ImG derived from an IEEE test feeder.

Keywords: Network analysis and control, Lyapunov methods, Electrical power systems
Abstract: In this paper we contribute a theoretical framework that sheds a new light on the problem of microgrid analysis and control. The starting point is an energy function comprising the kinetic energy associated with the elements that emulate the rotating machinery and terms taking into account the reactive power stored in the lines and dissipated on shunt elements. We then shape this energy function with the addition of an adjustable voltage-dependent term, and construct incremental storage functions satisfying suitable dissipation inequalities. Our choice of the voltage-dependent term depends on the voltage dynamics/controller under investigation. Several microgrids dynamics that have similarities or coincide with dynamics already considered in the literature are captured in our incremental energy analysis framework. The twist with respect to existing results is that our incremental storage functions allow for a large signal analysis of the coupled microgrid obviating the need for simplifying linearization techniques and for the restrictive decoupling assumption in which the frequency dynamics is fully separated from the voltage one.

Keywords: Electrical power systems, Energy systems, Control over networks
Abstract: The paper deals with the control of low-voltage microgrids with master/slave architecture. Distributed energy resources (DERs) are interfaced to the grid by means of conventional inverters (slave units), and a microgrid master controller (master unit) governs the interaction between the utility and the microgrid at the point of common coupling with the main grid. The power sharing among the available resources is achieved by the power-based control, a technique which allows to pursue both local (DER level) and global (microgrid level) optimization goals. The paper overviews and analyzes the control algorithm and focuses on how the considered approach can be employed to attain effective modes of operation in microgrids. Simulation results supporting the proposed approach are finally provided.

Keywords: Electrical power systems, Power electronics, Nonlinear system theory
Abstract: This paper studies the problem of existence and stability of equilibria of dc linear time–invariant circuits with constant power loads. First, we correct an unfortunate mistake in our previous work [10] pertaining to the sufficiency of the condition for existence of equilibria in multiport systems given there. Second, we give two necessary conditions for existence of equiibria. The first one is a simple linear matrix inequality hence it can be easily verified with existing software. Third, we prove that the latter condition is also sufficient if a set defined by the problem data is convex, which is the case for single and two–port systems. Finally, sufficient conditions for stability and instability for a given equilibrium point are given. The results are illustrated with two benchmark examples.

Keywords: Electrical power systems, Decentralized control, Lyapunov methods
Abstract: High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. When connecting multiple HVDC lines into a multi-terminal HVDC (MTDC) system, several challenges arise. To ensure safe and efficient operation of MTDC systems, the voltage of all terminals need to be steered to within an operational range. In this paper we study the commonly used decentralized voltage droop controller, and show that it in general does not steer the voltages to within the operational range. We propose a decentralized PI controller with deadband, and show that it always steers the voltages to within the operational range regardless of the loads. Additionally we show that the proposed controller inherits the property of proportional power sharing from the droop controller, provided that both the loads and the line resistances are sufficiently low. The results are validated through simulation in MATLAB.

Keywords: Maritime
Abstract: The control algorithm hierarchy of motion control for over-actuated mechanical systems with a redundant set of effectors and actuators commonly includes three levels. First, a high-level motion control algorithm commands a vector of virtual control efforts (i.e. forces and moments) in order to meet the overall motion control objectives. Second, a control allocation algorithm coordinates the different effectors such that they together produce the desired virtual control efforts, if possible. Third, low-level control algorithms may be used to control each individual effector via its actuators. Control allocation offers the advantage of a modular design where the highlevel motion control algorithm can be designed without detailed knowledge about the effectors and actuators. Important issues such as input saturation and rate constraints, actuator and effector fault tolerance, and meeting secondary objectives such as power efficiency and tear-and-wear minimization is handled within the control allocation algorithm. The objective of the presentation is survey control allocation algorithms. The survey classifies the different algorithms according to two main classes based on the use of linear or nonlinear models, respectively. The presence of physical constraints (e.g input saturation and rate constraints), operational constraints and secondary objectives makes optimization-based design a powerful approach. The simplest formulations allow explicit solutions to be computed using numerical linear algebra in combination with some logic and engineering solutions, while the more challenging formulations with nonlinear models or complex constraints and objectives call for iterative numerical optimization procedures and dynamic methods. Experiences using the different methods in marine vessel control application are discussed.

Keywords: Linear systems, Decentralized control, Agents and autonomous systems
Abstract: This paper describes the principles of a decentralized framework for the guaranteed collision avoidance of Multi-Agent dynamical systems sharing a common working space. The results are constructive and can be effective in the certification of mission safety. The geometric aspects of the collision avoidance problem are exploited to define the control policies. The main contributions are related to the optimization-based decentralized feedback control which renders a so-called functioning zone controlled invariant. An illustrative example is analyzed in order to highlight the effectiveness of the proposed approaches.

Keywords: Mechatronics, Differential algebraic systems, Nonlinear system theory
Abstract: In this paper, a new approach for dynamic modeling and the controller design of an omniwheel mobile platform with respect to high dynamic requirements is proposed. Compared with the previous articles, the tire model and the electrical machines are taken into account. The entire dynamic model is derived as a semi-explicit form of descriptor systems, which treats the tire forces and the torques of the electrical machines as fictitious inputs. It is possible to parameterize all the state variables, the constraints and inputs with the corresponding structure coordinates and their derivatives analytically. Due to the property of differential parameterization, the design of the decoupling controller can be achieved easily by transforming the overall system in Brunovsky normal form. By introducing additional coupling conditions, the electrical machines can work in optimum condition with respect to energetic aspects to generate the desired torque for driving.

Keywords: Autonomous robots, UAV's, Cooperative control
Abstract: This paper presents a bounded formation controller for multiple quadrotors (UAVs) system with leaderfollower structure. Considering the actuator saturation of the quadrotors, the hyperbolic function is used in the formation controller design. The composite nonlinear feedback is integrated in the formation controller in order to improve the formation performance. The simulation and experimental results show that the formation task is achieved with small overshoot and rapid response speed.

Keywords: Concensus control and estimation, Observers for nonlinear systems, Output feedback
Abstract: Design of observers and observer-based output feedback consensus controllers for continuous-time strict-feedback multi-agent systems with sampled observation is considered. First continuous-time observers for continuous-time multi-agent systems and discrete-time observers for their exact (discrete-time) models are designed. Then output feedback consensus controllers are constructed by combining the designed observers and state feedback consensus controllers. A numerical example is given to illustrate the proposed design method.

Keywords: Network analysis and control, Agents networks, Control over networks
Abstract: Two optimal leader selection problems are examined for multi-agent networks. The optimal leader set is the set of m > 0 leaders that maximizes performance of a linear dynamic network. In the problem for controllability, each leader is identified with a control input, and performance is measured by average controllability and reachable subspace volume. In the problem for robustness, each leader responds to an external signal, the linear dynamics are noisy, and the performance is measured by the steady-state system error. Previously, we showed that the optimal leader set for robustness maximizes a joint centrality in the network graph. In this paper, we show how the optimal leader set for controllability depends also on measures of the graph, including information centrality of leaders and eigenvectors of the graph Laplacian. We explore a fundamental trade-off between optimal leader selection for controllability and for robustness, and we outline a distributed algorithm for the selection of a pair of leaders in trees.

Keywords: Mechatronics, Servo control, Manufacturing processes
Abstract: A positioning device for placing a magnetized component on a ferromagnetic plate without collision has been fabricated. When the magnetized component approaches to the plate, the attractive force between them increases sharply as the gap decreases. It sometimes causes them to collide. To prevent such collision, a force compensation control is applied to cancel such nonlinear disturbance force by the actuator driving the component. In addition, a command revision control is implemented to avoid collision even in the presence of errors in modeling and positioning. The effectiveness of the proposed control schemes is demonstrated experimentally.

Keywords: Predictive control for linear systems, Aerospace, Optimization
Abstract: This paper describes the design of a model predictive controller (MPC) for the longitudinal motion of a passenger aircraft. The main focus of this work is on the performance of the controller in terms of computation time required for online optimization. In particular, the controller must accomplish the following objectives: (i) run in real-time, i.e., return a command within the sampling time (only a few milliseconds) of the system, and (ii) rely only on simple algebraic operations, in view of future implementations on embedded platforms. We make use of our previously developed parallel dual fast-gradient (PDFG) solver to accomplish the aforementioned objectives. This solver combines operator-splitting and fast-gradient methods and has been successfully tested for regulation problems on academic examples. This work aims to extend the use of the proposed PDFG solver to tracking problems in practical applications, such as the one proposed in this paper. Our results motivate a more extensive investigation of model predictive control techniques in fields with hard real-time constraints, such as aerospace or automotive.

Keywords: Predictive control for linear systems, Constrained control
Abstract: This paper shows how to construct and implement explicit MPC feedback laws for systems with a large number of states. Specifically, the construction of critical regions of the explicit MPC solution is avoided altogether and is instead replaced by a two-step procedure. In the first step, all optimal active sets are enumerated off-line and the corresponding KKT matrices are pre-factored. Then, in the on-line step, the optimal control inputs are identified by checking primal and dual feasibility conditions using the pre-factored data. The advantage of such an approach is that it allows to construct explicit MPC solutions even for complex systems. The feasibility of the approach is demonstrated on a laboratory distillation column described by a dynamical model with 10 state variables. We show that the control algorithm requires only modest computational resources on-line. The performance of the proposed regionless explicit MPC strategy is validated using experimentally collected data. The paper also covers identification of the dynamical behavior of the distillation column and the design of a suitable state observer.

Keywords: Optimal control, Differential algebraic systems
Abstract: Airborne Wind Energy (AWE) concerns systems capable harvesting energy from the wind, offering an efficient alternative to traditional wind turbines by flying crosswind with a tethered airfoil. Such concepts involve a system more difficult to control than conventional wind turbines. These systems generally cannot be operated efficiently in very low wind conditions, necessitating intervention by launching and landing. In contrast to this approach, this paper proposes to continue flying holding patterns which minimize power consumption. Efficient holding patterns are determined by solving an optimal control problem. The model is specified as a set of differential algebraic equations and an approximation of the tether drag is taken into account. Finally, an evaluation in terms of energy is performed by means of statistical approach.

Keywords: Distributed cooperative control over networks, Cooperative autonomous systems, Optimization
Abstract: This work presents an online distributed motion planning strategy for cooperating vehicles. The motion planning is formulated as an optimization problem that returns smooth trajectories. These are parameterized as splines, which allows a representation with a limited number of variables and enables guaranteed constraint satisfaction with a finite set of constraints. The computations for solving the problem are distributed among the agents by using the Alternating Direction Method of Multipliers (ADMM). In order to cope with a dynamic environment and disturbances, the algorithm is formulated in a receding horizon fashion, such that the future part of a motion trajectory is reoptimized iteratively. The required update time and the amount of inter-agent communication are reduced by performing only one ADMM iteration per update. In this way the method converges over the subsequent path updates. Simulations with a formation of holonomic vehicles in a dynamic environment demonstrate the capability of the proposed approach to generate optimal trajectories at an update rate of 20 Hz.

Keywords: Autonomous systems, Optimal control, Mechatronics
Abstract: Safe operation of autonomous systems demands a collision-free motion trajectory at every time instant. This paper presents a method to calculate time-optimal motion trajectories for autonomous systems moving through an environment with both stationary and moving obstacles. To transform this motion planning problem into a small dimensional optimization problem, suitable for real-time optimization, the approach (i) uses a spline parameterization of the motion trajectory; and (ii) exploits spline properties to reduce the number of constraints. Solving this optimization problem with a receding horizon allows dealing with modeling errors and variations in the environment. In addition to extensive numerical simulations, the method is experimentally validated on a KUKA youBot. The average solving time of the optimization problem in the experiments is 0.05s, which is sufficiently fast for correcting deviations from the initial trajectory.

Keywords: Automotive, Predictive control for linear systems, Uncertain systems
Abstract: This paper presents a comparison between two approaches addressing vehicle lateral dynamics control. In the framework of Auto-Steering for target tracking application, Model Predictive Control (MPC) and Interpolation Based Control (IBC) are studied on a similar model-based design. Both control strategies are of interest by their ability to treat problem constraints and actuator limits in a systematic manner, as well as their capability to include changes of the behavior when the speed of the vehicle changes, yielding a linear parameter varying system. Speed variation for the MPC controller brings an uncertain model, that will be described by a polytopic class of dynamics. Thanks to the online measurement of the parameter, the system dynamics will be computed at each sample time to solve the optimization problem. Parameter-dependent Lyapunov functions and positive set invariance theory are used to ensure stability and feasibility. Interpolation Based control is a different approach, whose principle is to use a control action constructed as an interpolation between two computed extreme values. Each time, two linear programming problems are solved, which makes this approach to be a suitable trade-off between performance and computation cost.

Keywords: Computational methods, Optimal control, Optimization algorithms
Abstract: This paper presents an indirect method for the numerical solution of optimal control problems that may contain control variable inequality constraints (CVICs), and state variable inequality constraints (SVICs). An approximate solution to the problem is found by solving a sequence of boundary value problems (BVPs) involving differential-algebraic equations (DAEs). Here, the complementarity conditions associated with the inequality constraints are approximated using Kanzow's smoothed Fischer-Burmeister formula. The paper shows that this approach leads to DAEs that have differentiation index 1. Moreover, this index-1 condition holds even in the case where higher-order SVICs are present. The efficacy of the algorithm is established by examining optimal control problems that contain CVICs and SVICs. The numerical evaluation includes a comparison of the proposed noninterior method and a Newton interior-point method for the solution of the index-1 BVP-DAEs.

Keywords: Optimal control, H2/H-infinity methods, Large-scale systems
Abstract: This paper presents a novel gradient based iterative approach to concurrently optimize plant and controller parameters. The co-design approach is linear matrix inequality (LMI) based and relies on estimates of the differential properties of the objective function with respect to the design variables which are obtained by using the dual solution to the control design problem. Contrary to most existing techniques which assume an affine dependency of the objective function on the optimization problem, the presented approach allows for nonlinear dependency, and hence can handle a broader class of co-design problems. Moreover, unlike other gradient based techniques, the method doesn't need to compute controller parameters at each iteration. The developed method is validated using numerical examples of a gantry machine and an electric motor.

Keywords: Optimal control, Robotics
Abstract: Tracking a moving target is often of interest in surveillance, automated guidance and leader-follower strategies in networked agents. In this paper, an optimal navigation scheme has been devised for moving target tracking in presence of obstacles; a problem one usually finds in a real-life scenario. The theoretical formulation of the problem has been developed and optimal candidate solutions have been sought in the light of Pontryagin's Maximum Principle. Simulation results presented conform to the necessary conditions for optimality.

Keywords: Optimal control, Stochastic control, Large-scale systems
Abstract: The simplicity of Approximate Dynamic Programming offers benefits for large-scale systems compared to other synthesis and control methodologies. A common technique to approximate the Dynamic Program, is through the solution of the corresponding Linear Program. The major drawback of this approach is that the online performance is very sensitive to the choice of tuning parameters, in particular the state relevance weighting parameter. Our work aims at alleviating this sensitivity. To achieve this, we propose to find a set of approximate Q-functions, each for a different choice of the tuning parameters, and then to use the pointwise maximum of the set of Q-functions for the online policy. The pointwise maximum promises to be better than using only one of individual Q-functions for the online policy. We demonstrate that this approach immunizes against tuning errors through a stylized portfolio optimization problem.

Keywords: Optimization, Autonomous systems, Constrained control
Abstract: This paper develops a method for the construction of consistently improving inner and outer approximate polytopic sets for controllability and reachability under constraints. Sequences of consistently improving approximate polytopic sets are obtained from the solution of a series of Second Order Cone Programming (SOCP) problems. Notable advances in reliability and speed of recent SOCP solvers render the proposed procedure computationally attractive, since the solutions to frequently encountered SOCPs are computable in tens of milliseconds or less. The initialization of the previous algorithm is enhanced by means of a simultaneous computation of an optimized pair of inner and outer bounding simplices. The Hausdorff distance is employed as a criteria for the growth of the inner and outer approximate polytopic sets as well as a topologically suitable metric for convergence. The algorithm yields polytopes that inner and outer approximate exact Controllable/Reachable (C/R) set to a desired precision w.r.t. the Hausdorff distance. The relevance and value of the proposed procedure are demonstrated by its application to a fully constrained Mars planetary landing problem.

Keywords: Optimization algorithms, Filtering, Sensor and signal fusion
Abstract: In Moving Horizon Estimation (MHE) the computed estimate is found by solving a constrained finite-time optimal estimation problem in real-time at each sample in a receding horizon fashion. The constrained estimation problem can be solved by, e.g., interior-point (IP) or active-set (AS) methods, where the main computational effort in both methods is known to be the computation of the search direction, i.e., the Newton step. This is often done using generic sparsity exploiting algorithms or serial Riccati recursions, but as parallel hardware is becoming more commonly available the need for parallel algorithms for computing the Newton step is increasing. In this paper a newly developed tailored, non-iterative parallel algorithm for computing the Newton step using the Riccati recursion for Model Predictive Control (MPC) is extended to MHE problems. The algorithm exploits the special structure of the Karush-Kuhn-Tucker system for the optimal estimation problem. As a result it is possible to obtain logarithmic complexity growth in the estimation horizon length, which can be used to reduce the computation time for IP and AS methods when applied to what is today considered as challenging estimation problems. Furthermore, promising numerical results have been obtained using an ANSI-C implementation of the proposed algorithm, which uses Message Passing Interface (MPI) together with InfiniBand and is executed on true parallel hardware. Beyond MHE, due to similarities in the problem structure, the algorithm can be applied to various forms of on-line and off-line smoothing problems.

Keywords: Nonlinear system identification, Delay systems, Optimization algorithms
Abstract: According to the Hierarchical identification principle, the auxiliary model approach and the rounding properties, we derive a recursive algorithm for the identification of Wiener time delay systems. The main idea of the proposed algorithm consists in decomposing the nonlinear cost function into two cost functions. The gradient and the Levenberg-Marquardt approaches are then used to minimize these cost functions in order to estimate simultaneously the time delay and the system parameters of the linear and the nonlinear blocks. The convexity condition to authorize the use of the rounding property is also developed. A simulation example is finally presented to illustrate the effectiveness of the proposed method.

Keywords: Identification for control
Abstract: Block-oriented system identification allows to define physically meaningful connection points between logically separated parts of a system. This work presents a class of systems which allow to apply a simple way of data-based modelling. The definition of the class via a few key properties is given, as well as the general idea for the identification approach. Afterwards it is show, that the very common system of a hydraulic motion control with servo pumps fits into this system class and the presented method is applied and verified in a simulation example.

Keywords: Linear parameter-varying systems, Nonlinear system identification
Abstract: Least Squares Support Vector Machine (LS-SVM) is a computationally efficient kernel-based regression approach which has been recently applied to nonparametric identification of Linear Parameter Varying (LPV) systems. In contrast to parametric LPV identification approaches, LS-SVM based methods obviate the need to parameterize the scheduling dependence of the LPV model coefficients in terms of a-priori specified basis functions. However, an accurate selection of the underlying model order (in terms of number of input lags, output lags and input delay) is still a critical issue in the identification of LPV systems in the LS-SVM setting. In this paper, we address this issue by extending the LS-SVM method to sparse LPV model identification, which, besides nonparametric estimation of the model coefficients, achieves datadriven model order selection via convex optimization. The main idea of the proposed method is to first estimate the coefficients of an over-parameterized LPV model through LS-SVM. The estimated coefficients are then scaled by polynomial weights, which are shrunk towards zero to enforce sparsity in the final LPV model estimate. The properties of the proposed approach are illustrated via simulation examples.

Keywords: Linear systems, Identification
Abstract: Kernel-based regularization techniques are constantly gaining attention in the identification world, due to their success in modeling the impulse response of linear systems. In this work, the same problem is considered from a different perspective. Instead of including prior knowledge in the definition of the covariance matrix of the parameters, here the focus is on the cost function level. The key idea is to define the regularization matrix as a filtering operation on the parameters, which allows for a more intuitive formulation of the problem from an engineering viewpoint. Moreover, this results in an effective user-friendly method to model a wide range of systems, including low-pass, band-pass and high-pass systems. The effectiveness of the proposed approach is illustrated by means of Monte Carlo simulations on five linear modeling examples, where the filter-based regularization outperforms the existing method based on the TC and DC kernels.

Keywords: Optimization, Identification for control, Optimization algorithms
Abstract: We consider the input design problem of finding the minimal required experiment time such that accuracy constraints on the parameter estimate of an identification experiment are satisfied, while also respecting signal amplitude bounds. The input signal is parameterized as a multi-sine. We first show how multiple linear matrix inequalities from the least-costly and applications-oriented experiment design frameworks can be transformed into a generalised E-optimality constraint. Then, the solution to our problem is found by: (i) designing a multi-sine of one period with the Guillaume- Manchester algorithm [11], [9] that minimises the generalised E-optimality criterion under signal amplitude bounds, and (ii) utilising periodicity and an optimality condition to scale the experiment time such that the imposed accuracy constraints are also respected. An example shows an experiment time reduction of 54% compared with a traditional least-costly experiment design approach.

Keywords: Switched systems, Constrained control, Lyapunov methods
Abstract: This paper presents a design approach for observer-based relay feedback controllers. A switching law dependent on the estimation state is designed while using a Luenberger observer. The stabilization problem leads to qualitative conditions. A numerical example is provided to assess the effectiveness of the developed method.

Keywords: Cooperative control, Neural networks, Adaptive control
Abstract: In this paper, an adaptive synchronization problem is considered for an array of linearly coupled reaction-diffusion neural networks with antagonistic interactions. Firstly, the interaction topology among the the neurons is modeled by a signed graph. The state evolution of a neuron in each layer of neural networks is described by a reaction-diffusion equation with Dirichlet boundary conditions. Further, the collective dynamics of the multi-layer neural networks is built as a coupled reaction-diffusion equation with both spatial diffusion coupling and state coupling. When the interactions between neurons suffer from time-varying delays, an edge-based adaptive strategy is designed to tune the coupling weights of the network and an anti-synchronization control is developed by using only local information of neighboring nodes to achieve anti-synchronization. A sufficient condition is given to guarantee anti-synchronization with the help of a Lyapunov function method and the structural balance condition. Some simulation results are provided to demonstrate the effectiveness of the proposed adaptive control strategy.

Keywords: Delay systems, Identification for control, Nonlinear system identification
Abstract: It is proposed a first step to the model-based closed-loop control of a separated flow. In such situations, fluid mechanics phenomena are highly nonlinear and can be represented by means of the Navier-Stokes equations. However, such a model still rises difficult issues for control practice. This paper proposes an alternative, bilinear and delayed model, the accuracy of which is studied. The identification technique combines least-square technique with a Mesh Adaptive Direct Search (MADS) algorithm. The main feature of the model is state dependent structure of input delay.

Keywords: Delay systems, Linear systems, H2/H-infinity methods
Abstract: This paper deals with the Hinf state-feedback control synthesis for time-delay linear systems. We extend the use of the finite order LTI system, called comparison system, to design a controller dependent not only on the state at the present time and maximum delay, but also on an arbitrary number of values between those. Therefore, we are able to increase the maximum stable delay without increasing the buffer used to implement the controller. All methods presented here consider time-delay systems control design with classical numeric routines based on Riccati equations and H1 theory. An illustrative example is presented.

Keywords: Delay systems, Observers for nonlinear systems, Observers for linear systems
Abstract: New design of interval observers for continuous-time systems with discrete-time measurements is proposed. Positivity and stability conditions are obtained using the time-delay approach. Next, control is synthesized based on interval estimates. Efficiency of the obtained solution is demonstrated on examples.

Keywords: Delay systems
Abstract: This paper studies the migration pattern of characteristic imaginary roots of multiplicity three and four in time-delay systems with two delays when the delay parameters undergo small deviations. Stability analysis for such problems is often based on Puiseux series, as multiple roots are not differentiable with respect to delay parameters. However, in this paper the approach is more traditional without using Puiseux series. In the case of triple roots, we show that the stability crossing curves are smooth; when a perturbation occurs in the delay parameter space, two roots move to one half-plane and one root to the other half-plane. The case of quadruple root is more complicated as the stability crossing curve has a cusp. Thus, in the neighbourhood of the critical point, the delay parameter space is divided in an S-sector and a G-sector. When the parameters move into the G-sector, two roots move to the right half-plane, and the other two roots move to the left half-plane. When the parameters move into the S-sector, then three of the roots move to one half-plane, and the remaining root moves to the other half-plane, depending on the conditions.

Keywords: Agents and autonomous systems, Distributed cooperative control over networks, Delay systems
Abstract: This work investigates performance of noisy time-delayed linear consensus networks from a graph topological point of view. Performance of the network is measured by the square of the H_2-norm of the system. The focus of this paper is on noisy consensus networks with homogeneous time delays affecting both the agent and all its neighbors. We derive an exact expression for the performance measure of the network in terms of time delay parameter and Laplacian eigenvalues of the underlying graph of the network. It is shown that the performance measure is a convex and Schur-convex function of Laplacian eigenvalues. We characterize the network topology with optimal performance. Furthermore, we quantify a fundamental limit on the best achievable performance based on performance of the optimal topology.

Keywords: Filtering, Stochastic filtering, Uncertain systems
Abstract: This paper addresses the state estimation problem for nonlinear systems with parameter uncertainties. Firstly, we analyze the influence which the parameter uncertainties have on covariance matrix to a mean square error, and derived robust UKF (RUKF). The RUKF is less sensitive to deviations, and more accurate than conventional UKF. However, the estimated values of the RUKF can have some offsets by the influence of parameter uncertainties. Then we also analyze the influence which the parameter uncertainties have on predictive estimate, and develop new estimation gain to reduce the influence of the parameter uncertainties. We call this new robust filtering method as Gain-Constrained RUFK (GC-RUKF). The validity of the proposed methods is illustrated by Monte Carlo simulations.

Keywords: Filtering, Markov processes, Autonomous systems
Abstract: In this work, we consider the problem of using a noisy binary sensor to optimally track a target that moves as a Markov Chain in a finite discrete environment. Our approach focuses on one-step optimality because of the apparent infeasibility of computing an optimal policy via dynamic programming. We prove that, under mild assumptions, always searching in the second most likely location minimizes one-step variance while maximizing the belief about the target's location over one step. Simulation results demonstrate the performance of our strategy and suggest the policy performs well over arbitrary horizons.

Keywords: Filtering, Observers for nonlinear systems, Stochastic filtering
Abstract: We propose two variants of the Linearized Kalman Filter (LKF). The model linearization is made about an auxiliary state estimate that can be seen as an exogenous input to the LFK, and the resulting two-stage estimator is called an exogenous Kalman filter (XKF). Since the linearized model of the LKF does not depend on the estimate from the LKF, it follows from stability theory of cascades that the stability properties of the XKF are inherent from the auxiliary state estimator, since the nominal LKF is globally exponentially stable. In some cases, the use of nonlinear transforms and immersions can be used to render the nonlinear dynamics into a globally valid linear time-varying (LTV) form that can be used for design of the auxiliary state estimator. Even though the noise and disturbances may be influenced in a non-favorable way by such transforms, they allow the auxiliary state estimator to be designed using a time-varying Kalman filter, leading to a two-stage estimator called the Double Kalman Filter (DKF). The DKF is inherently globally exponentially stable for nonlinear systems that can be transformed into uniformly observable LTV systems. The XKF and DKF overcome the potential divergence of the extended Kalman Filter (EKF) and similar algorithms that can result from inaccurate initialization, by applying a feed-forward/cascade structure instead of the feedback inherent in the EKF linearization. The method is illustrated using examples.

Keywords: Filtering, Stochastic systems, Chemical process control
Abstract: This paper presents two accurate continuous-discrete extended Kalman filters designed for estimating stiff continuous-time stochastic models in chemical engineering. These methods are grounded in the Gauss-type nested implicit Runge-Kutta formulas of orders 4 and 6, which are applied for treating moment differential equations (MDEs). The local and global error controls implemented in these filters ensure that the MDEs are integrated with negligible errors, numerically. The latter raises the accuracy of state estimation and makes our state estimators more effective than the traditional extended Kalman filter based on the Euler-Maruyama discretization of order 0.5 and the continuous-discrete cubature Kalman filter grounded in the Ito-Taylor approximation of order 1.5. The variable-stepsize fashion of these new filtering techniques allows also for the accurate state estimation of chemical stochastic models with infrequent measurements. The designed state estimators are examined numerically on the stochastic Oregonator model, which is a famous stiff example in chemistry research.

Keywords: Observers for nonlinear systems, Stability of nonlinear systems, Lyapunov methods
Abstract: Exponentially Bounded-Input-Bounded-State and Bounded-Input-Bounded-Output (BIBO) stability of the State Dependent Differential Riccati Equation (SDDRE) based observer of deterministic nonlinear time-varying systems is proved by three approaches. Each proof highlights different aspect of the SDDRE based estimator-observer stability. The proofs use the State Dependent Coefficient (SDC) form representation of nonlinear system. One approach uses results from theory of linear time-varying systems. The second approach defines Lyapunov function and uses LaSalle's invariance principle and the new invariance principle to show that the state of the SDDRE based estimator is BIBO stable. The third approach proves that the state transition matrix of the estimator is exponentially stable under specific conditions and computes bounds on the state. It is shown that uniform complete observability and controllability along the system's trajectories are sufficient for asymptotic stability.

Keywords: Observers for nonlinear systems, Stochastic filtering, Stochastic systems
Abstract: In this paper, we propose a new method for implementation of a High-Gain Observer (HGO) to cope with measurement noise through Stochastic Approximation (SA). Most approaches have been using a trade-off between a speed of regeneration of states in the presence of uncertainties and the effect of measurement noise. Through SA, we are able to reserve authentic properties of the HGO i.e., a fast reconstruction of system states and robustness to uncertainties, while dealing with the effect of measurement noise both in practical and analytical manners. Regularity conditions are verified to analyze the stability by the associated Ordinary Differential Equation (ODE), i.e., the ODE method. Stability analysis of the full system is conducted. Numerical simulation results demonstrate the validity of the proposed design method.

Keywords: Computational methods, Fault detection and identification, Neural networks
Abstract: The use of false or erroneous data can lead to wrong decisions when operating a system. In case of a water distribution network, the use of incorrect data could lead to errors in the billing system, waste of energy, incorrect management of control elements, etc. This paper is focused on detecting flow meters reading abnormalities by exploiting the temporal redundancy of the demand time series by means of artificial neural networks (ANN). Communication problems with the sensor generate missing data and bad maintenance service in the flow meters produce false data. In this work, a methodology to detect the false data (validate) and replace the missing or false data (reconstruct) is proposed. As a core methodology, ANNs are used to model the time series generated from the water demand flow meters, and use the confidence intervals to validate the information. To illustrate the proposed methodology, the application to flow meters in the water distribution network of Barcelona is used

Keywords: Fault diagnosis, Large-scale systems
Abstract: In this paper, a decentralized fault diagnosis algorithm for large scale system is proposed. The fault diagnosis algorithm starts from obtaining of ARRs (analytical redundancy relations) from a model. These analytical redundancy relations are converted into a graph, this graph is divided into various subgraphs using partition algorithm. From various subgraphs, different fault signature matrices are obtained and finally using various fault signature matrices and applying observer method a fault or faults are detected and isolated in large scale system. Entire proposed distributed fault diagnosis algorithm is divided into 5 different blocks. In order to illustrate the application of the proposed algorithm, a case study based on the Barcelona drinking water network (DWN) is used.

Keywords: Fault diagnosis
Abstract: This paper presents a new method for leak localization in Water Distribution Networks (WDNs) that uses a model based approach combined with Bayesian reasoning. Probability distribution functions in model-based pressure residuals are calibrated off-line for all the possible leak scenarios using a hydraulic simulator where leak size uncertainty, demand uncertainty and sensor noise are considered. A Bayesian reasoning is applied on-line to the available residuals to determine the location of leaks present in the WDN. A time horizon method combined with the Bayesian reasoning is also proposed to improve the accuracy of the leak localization method. The Hanoi DMA case study is used to illustrate the performance of the proposed approach.

Keywords: Nonlinear system theory, Lyapunov methods, Stability of nonlinear systems
Abstract: We strive to prove stability of a hydraulic network, where the pressure at the end user is controlled with PI control. The non-polynomial model is represented by numerous polynomial systems defined on sub-sets of R^n. The sub-sets are defined by compact basic semi-algebraic sets. The stability of the PI-controller is proved by designing a Lyapunov function which fulfils different criteria in different sub-sets of R^n. We find a polynomial Lyapunov function for the system using SOSTOOLS supported by Putinar’s Positivstellensatz.

Keywords: Predictive control for nonlinear systems, Transportation systems, Energy systems
Abstract: This paper investigates the modelling and predictive control of a drinking water supply network with the aim of minimising the energy and economic cost. A model predictive controller, MPC, is applied to a nonlinear model of a drinking water network that follows certain constraints to maintain consumer pressure desire. A model predictive controller, MPC, is based on a simple model that models the main characteristics of a water distribution network, optimizes a desired cost minimisation, and keeps the system inside specified constraints. In comparison to a logic (on/off) control design, controlling the drinking water supply network with the MPC showed reduction of the energy and the economic cost of running the system. This has been achieved by minimising actuator control effort and by shifting the actuator use towards the night time, where energy prices are lower. Along with energy cost reduction the MPC also achieves reduction in the amount of consumed water by keeping the pressure closer to the lower pressure constraint.

Keywords: Robust control, Predictive control for linear systems, Large-scale systems
Abstract: In this paper we propose to apply a novel robust predictive controller for tracking periodic references following a constraint tightening procedure to an uncertain discrete time algebraic-differential linear model of a large scale drinking water network. The system considered has been obtained from the water balance equations of a section of Barcelona’s drinking water network taking into account bounded additive perturbations. In this model, we assume that a prediction of the water demand is available and that the prediction error is bounded. The controller guarantees that the perturbed closedloop system converges asymptotically to the optimal reachable periodic trajectory, robust constraint satisfaction and recursive feasibility. To demonstrate the main properties of the controller three different simulation scenarios have been considered.