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This paper investigates the distributed model predictive control (DMPC) problem for multiple dynamically-decoupled heterogeneous linear systems subject to both local state and input constraints and coupled non-convex constraints (e.g., collision avoidance constraints). To solve the resulting non-convex optimal control problem (OCP) at each time step, successive convex approximation (SCA) technique is a promising convexification approach. However, an algorithm that is fully distributed, computationally efficient, and recursively feasible for both local and coupled non-convex constraints remains an open problem. In this paper, we propose an inner–outer layer framework that integrates three important modifications into the SCA scheme for solving each OCP. Specifically, (i) in the inner layer, we utilize a distributed dual fast gradient approach to enable the distributed execution, (ii) as for the outer layer, instead of requiring the optimal solution at each iteration by classical SCA scheme, we improve computational efficiency by relying solely on a suboptimal solution achieved through flexible termination, and (iii) an adaptive tightening strategy imposing on the convexified coupled constraints is developed which permits both the inner and outer layers to terminate in advance with the guarantee of the closed-loop non-convex coupled constraints satisfaction. Under some reasonable assumptions, convergence of the proposed inner–outer layer framework, recursive feasibility of the proposed DMPC algorithm and stability of the resulting whole closed-loop system are ensured. Simulation results on multi-agent control with non-convex coupled collision avoidance constraints and comparisons against some benchmark solutions using the centralized method are carried out to verify the performance of the proposed DMPC method. [ABSTRACT FROM AUTHOR]

Many practical applications in control require that constraints on the inputs and states of the system are respected, while some performance criterion is optimized. In the presence of model uncertainties or disturbances, it is often sufficient to satisfy the state constraints for at least a prescribed share of the time, such as in building climate control or load mitigation for wind turbines. For such systems, this paper presents a new method of Scenario-Based Model Predictive Control (SCMPC). The basic idea is to optimize the control inputs over a finite horizon, subject to robust constraint satisfaction under a finite number of random scenarios of the uncertainty and/or disturbances. Previous SCMPC approaches have suffered from a substantial gap between the rate of constraint violations specified in the optimal control problem and that actually observed in closed-loop operation of the controlled system. This paper identifies the two theoretical explanations for this gap. First, accounting for the special structure of the optimal control problem leads to a substantial reduction of the problem dimension. Second, the probabilistic constraints have to be interpreted as average-in-time, rather than pointwise-in-time. Based on these insights, a novel SCMPC method can be devised for general linear systems with additive and multiplicative disturbances, for which the number of scenarios is significantly reduced. The presented method retains the essential advantages of the general SCMPC approach, namely a low computational complexity and the ability to handle arbitrary probability distributions. Moreover, the computational complexity can be adjusted by a sample-and-remove strategy. [ABSTRACT FROM AUTHOR]

Reducing the computation time of model predictive control (MPC) is important, especially for systems constrained by many state constraints. In this paper, we propose a new online constraint removal framework for linear systems, for which we coin the term constraint-adaptive MPC (ca-MPC). In so-called exact ca-MPC, we adapt the imposed constraints by removing, at each time-step, a subset of the state constraints in order to reduce the computational complexity of the receding-horizon optimal control problem, while ensuring that the closed-loop behavior is identical to that of the original MPC law. We also propose an approximate ca-MPC scheme in which a further reduction of computation time can be accomplished by a tradeoff with closed-loop performance, while still preserving recursive feasibility, stability, and constraint satisfaction properties. The online constraint removal exploits fast backward and forward reachability computations combined with optimality properties. [ABSTRACT FROM AUTHOR]

This paper presents a Distributed Stochastic Model Predictive Control algorithm for networks of linear systems with multiplicative uncertainties and local chance constraints on the states and control inputs. The chance constraints are approximated via Cantelli's inequality by means of expected value and covariance. The cooperative control algorithm is based on the distributed Alternating Direction Method of Multipliers, which renders the controller fully distributedly implementable, recursively feasible and ensures point-wise convergence of the states. The aforementioned properties are guaranteed through a properly selected distributed invariant set and distributed terminal constraints for the mean and covariance. The paper closes with an example highlighting the chance constraint satisfaction, numerical properties and scalability of our approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a novel hierarchical model predictive control (MPC) strategy that guarantees overall system stability. This method differs significantly from previous approaches to guaranteeing overall stability, which have relied upon a multi-rate framework where the inner loop (low level) is updated at a faster rate than the outer loop (high level), and the inner loop must reach a steady state within each outer loop time step. In contrast, the method proposed in this paper is aimed at stabilizing the origin of an error system characterized by the difference between the inner loop state and the state specified by a full-order reference model. This makes the method applicable to systems with reduced levels of time scale separation. This paper proposes a framework for guaranteeing stability that leverages the use of the reference model, in conjunction with -contractive constraint sets for both the inner and outer loops. The effectiveness of the proposed reference model-based strategy is shown through simulation on an existing stirred-tank reactor problem, where we demonstrate that the MPC optimization problem remains feasible and that the system remains stable and continues to perform well when time scale separation between the inner and outer loops is reduced. [Copyright &y& Elsevier]

Abstract: The contribution of this paper is to establish computable necessary and sufficient conditions on the model structure and on the experiment under which the Prediction Error Identification (PEI) criterion has a unique global minimum. We consider a broad class of rational model structures whose numerator and denominator are affine in the unknown parameter vector; this class encompasses all classical model structures used in system identification. The main results in this paper rely on the standard assumption that the system is in the model set, while some intermediate results are valid even when this assumption does not hold (in particular and ). This is achieved by first establishing necessary and sufficient conditions on the model structure and on the experiment under which a global minimum is isolated; these conditions must hold locally, at the global minimum. A second contribution is to show that these conditions are equivalent to the nonsingularity of the information matrix at that minimum. For open loop identification and, with some additional constraints also for closed loop identification, the nonsingularity of the information matrix is then also equivalent to the uniqueness of the global minimum. [Copyright &y& Elsevier]

Abstract: This paper introduces the concepts of Dwell-Time invariant/contractive (DT-invariant/contractive) set, Constraint Admissible DT-invariant/contractive (CADT-invariant/contractive) set for a discrete-time switching system under dwell-time switching. Main contributions of this paper include a characterization for a DT-contractive set, an algorithm for the computation of the maximal CADT-invariant set, a necessary and sufficient condition for asymptotic stability of the origin of switching systems under dwell-time switching and computation of the minimal dwell-time needed for asymptotic stability of the origin. [Copyright &y& Elsevier]

This paper develops a robust self-triggered control algorithm for time-varying and uncertain systems with constraints based on reachability analysis. The resulting piecewise constant control inputs achieve communication reduction and guarantee constraint satisfactions. In the particular case when there is no uncertainty, we propose a control design with minimum number of samplings over finite time horizon. Furthermore, when the plant is linear and the constraints are polyhedral, we prove that the previous algorithms can be reformulated as computationally tractable mixed integer linear programs. The method is compared with the robust self-triggered model predictive control in a numerical example and applied to a robot motion planning problem with temporal constraints. [ABSTRACT FROM AUTHOR]

This paper focuses on the control of a cooperative system composed of an Unmanned Aerial Vehicle (UAV) and an Unmanned Ground Vehicle (UGV) manipulating an object. The two units are subject to input saturations and collaborate to move the object to a desired pose characterized by its position and inclination. The dynamics are derived using the Euler–Lagrange method. A stabilizing control law is proposed where the UGV is tasked to deploy the object to a certain position whereas the UAV adjusts its inclination. In particular, a proportional–derivative control law is proposed for the UGV, and a cascade control is used for the UAV, where the inner loop controls the attitude of the UAV and the outer loop stabilizes the inclination of the object. The stability of the points of equilibrium is proven using small gain arguments. To ensure constraints satisfaction at all times, a reference governor unit is added to this stabilizing control law. Simulations and experimental results are provided to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a multi-regulator control scheme for single-input systems, where the setpoint of a regulated output must be changed under the constraint that a set of minimum-phase outputs remain within prescribed bounds. The strategy is based on a max–min selector system frequently used in the aerospace field. The regulators used for the regulated and limited outputs are of the sliding mode type, where the sliding variable is defined as the difference between an output and its allowable limit. The paper establishes overall asymptotic stability, as well as invariance properties leading to limit protection. The design methodology is illustrated with a detailed simulation example on thrust control of a turbofan engine. [Copyright &y& Elsevier]

Abstract: An area traffic control network system is considered in this paper. Optimal signal settings can be determined while trip rates and network flow are in equilibrium. This problem can be formulated as a nonlinear mathematical program with equilibrium constraints. For the objective function, the system performance can be defined as a function of signal setting variables. For the constraint set, a user equilibrium traffic assignment with elastic demand obeying Wardrop’s first principle is formulated as a variational inequality problem. Due to the nonlinearity and non-differentiability of the perturbed solutions in equilibrium constraints, a non-smooth approach is investigated in this paper. Numerical tests are performed using a variety of example road networks to quantify the effectiveness and robustness of the proposed method. [Copyright &y& Elsevier]

Abstract: The guarantee of feasibility given feasibility at initial time is an issue that has been overlooked by many of the recent papers on stochastic model predictive control. Effective solutions have recently been proposed, but these carry considerable online computational load and a degree of conservativism. For the case that the elements of the random additive disturbance vector are independent, the current paper ensures that probabilistic constraints are met and that a quadratic stability condition is satisfied. A numerical example illustrates the efficacy of the proposed algorithm, which achieves tight satisfaction of constraints and thereby attains near-optimal performance. [Copyright &y& Elsevier]

This article investigates the problem of enforcing a virtual holonomic constraint (VHC) on a mechanical system with degree of underactuation one while simultaneously stabilizing a closed orbit on the constraint manifold. This problem, which to date is open, arises when designing controllers to induce complex repetitive motions in robots. In this paper, we propose a solution which relies on the parameterization of the VHC by the output of a double integrator. While the original control inputs are used to enforce the VHC, the control input of the double-integrator is designed to asymptotically stabilize the closed orbit and make the state of the double-integrator converge to zero. The proposed design is applied to the problem of making a PVTOL aircraft follow a circle on the vertical plane with a desired speed profile, while guaranteeing that the aircraft does not roll over for suitable initial conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the stability and performance of the standard least mean squares (LMS)-based consensus adaptive filters under a changing network topology. We first analyze the stability for possibly unbounded, non-independent and non-stationary signals, by introducing an information condition that can be shown to be not only sufficient but also necessary for the global stability. We also demonstrate that the distributed adaptive filters can estimate a dynamic process of interest from noisy measurements by a set of sensors working in a collaborative manner, in the natural scenario where none of the sensors can fulfill the estimation task individually. Furthermore, we give an analysis of the filtering error under various assumptions without stationarity and independency constraints on the system signals, and thus do not exclude applications to stochastic systems with feedback. In contrast to the analyses of the normalized LMS-based distributed adaptive filters, we need to use stochastic averaging theorems in the stability analysis due to possible unboundedness of the system signals. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive tracking control approach for a class of nonlinear state-constrained and time-varying delay systems with unknown time-varying control coefficients. As far as we know, there is no control method for such systems at present. To stabilize such a class of systems, the neural networks and a backstepping technique are utilized to structure an adaptive tracking controller. The Nussbaum gain technique is utilized to solve the problem of unknown time-varying control coefficients, and the Lyapunov–Krasovskii functionals (LKFs) are employed to eliminate the effect of unknown time-varying delays. In addition, the states are guaranteed to remain within their constraint sets based on the Barrier Lyapunov functions (BLFs). Finally, it can be proved that all signals in the closed-loop systems are bounded, the state constraints are never violated and the tracking errors fluctuate within the predetermined compact range around the zero. The simulation results are provided to illustrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Focusing on the trajectory curvature, this paper presents an innovative and analytical guidance law for the construction of geometrically convex trajectories. Moving along such trajectories, the lander can increase the probability of a safe landing in hazardous terrains. Initially, the curvature theorems of the powered descent trajectories are developed. In these theorems, the inner relationship between trajectory curvature and lander states is revealed, and the state constraints for a geometrically convex trajectory are derived. Next, the trajectory curvature guidance is developed in an analytical formulation by satisfying the state constraints for a convex trajectory, and the selection of the key guidance parameters is investigated. Finally, the performance of the trajectory curvature guidance is analyzed in detail, illustrating its superior hazard avoidance and the camera’s field of view. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to bounded-error state estimation involving time uncertainties. For a given bounded observation of a continuous-time non-linear system, it is assumed that neither the values of the observed data nor their acquisition instants are known exactly. For systems described by state-space equations, we prove theoretically and demonstrate by simulations that the proposed constraint propagation approach enables the computation of bounding sets for the systems’ state vectors that are consistent with the uncertain measurements. The bounding property of the method is guaranteed even if the system is strongly non-linear. Compared with other existing constraint propagation approaches, the originality of the method stems from our definition and use of bounding tubes which enable to enclose the set of all feasible trajectories inside sets. This method makes it possible to build specific operators for the propagation of time uncertainties through the whole trajectory. The efficiency of the approach is illustrated on two examples: the dynamic localization of a mobile robot and the correction of a drifting clock. [ABSTRACT FROM AUTHOR]

Data-driven predictive control (DDPC) has been recently proposed as an effective alternative to traditional model-predictive control (MPC) for its unique features of being time-efficient and unbiased with respect to the oracle solution. Nonetheless, it has also been observed that noise may strongly jeopardize the final closed-loop performance, since it affects both the data-based system representation and the control update computed from the online measurements. Recent studies have shown that regularization is potentially a successful tool to counteract the effect of noise. At the same time, regularization requires the tuning of a set of penalty terms, whose choice might be practically difficult without closed-loop experiments In this paper, by means of subspace identification tools, we pursue a three-fold goal: (i) we set up a unified framework for the existing regularized data-driven predictive control schemes for stochastic systems; (i i) we introduce γ -DDPC, an efficient two-stage scheme that splits the optimization problem in two parts: fitting the initial conditions and optimizing the future performance, while guaranteeing constraint satisfaction; (i i i) we discuss the role of regularization for data-driven predictive control, providing new insight on when and how it should be applied. A benchmark numerical case study finally illustrates the performance of γ -DDPC, showing how controller design can be simplified in terms of tuning effort and computational complexity when benefiting from the insights coming from the subspace identification realm. [ABSTRACT FROM AUTHOR]

For discrete-time linear systems subject to multiplicative disturbance described by random variables, we develop a sampling-based Stochastic Model Predictive Control algorithm. Unlike earlier results employing a scenario approximation, we propose an offline sampling approach in the design phase instead of online scenario generation. The paper highlights the structural difference between online and offline sampling and provides rigorous bounds on the number of samples needed to guarantee chance constraint satisfaction. The approach does not only significantly speed up the online computation, but furthermore allows to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided. Under mild assumptions, asymptotic stability of the origin can be established. [ABSTRACT FROM AUTHOR]

This paper explores the output-constrained tracking control problem for unknown Euler–Lagrange systems subject to actuator faults, in the case where the reference trajectory is unknown in advance. The presence of actuator faults may lead to the loss of strong controllability of the system assumed in the existing literature on robust control of multi-input multi-output nonlinear systems. The lack of a priori knowledge on the reference trajectory renders the current constraint-handling techniques to achieve prescribed tracking accuracy infeasible. To conquer the above obstacles, a novel fault compensation scheme is designed in this paper, and a new-type error boundary is introduced to the control design. It is proved that the proposed approach guarantees output tracking with prescribed accuracy and constraint satisfactions simultaneously, even if actuator faults occur. A comparative simulation on a robot manipulator is conducted to further illustrate the established theoretical findings. [ABSTRACT FROM AUTHOR]

To facilitate the real-time implementation of nonlinear model predictive control (NMPC), this paper proposes a deep learning-based NMPC scheme, in which the NMPC law is approximated via a deep neural network (DNN). To optimize the DNN controller, a novel "optimize and train" architecture is designed, where the processes of data generation and neural network training are combined together to result in a single large-scale stochastic optimization problem. Unlike the conventional "optimize then train" approach, our proposed one directly optimizes the closed-loop performance of the DNN controller over a finite horizon for a number of initial states. The important features of our proposed scheme are that it can deal with set-valued optimal MPC input, and a probabilistic guarantee of constraint satisfaction can be concluded for the closed-loop system without simulating the DNN controller. With our proposed scheme, an increased number of training scenarios leads to improved constraint satisfaction of the derived DNN controller, which is not necessarily true for the "optimize then train" approach. Statistical approaches for validating closed-loop control performance are also discussed. Furthermore, computational methods are introduced to efficiently solve the resulting stochastic optimization problem. The effectiveness of the proposed scheme is extensively illustrated with several numerical simulations. Compared with the conventional "optimize then train" approach, our proposed approach exhibits better closed-loop constraint satisfaction for all considered case studies. [ABSTRACT FROM AUTHOR]

Safety-critical control is characterized as ensuring constraint satisfaction for a given dynamical system. Recent developments in zeroing control barrier functions (ZCBFs) have provided a framework for ensuring safety of a superlevel set of a single constraint function. Euler–Lagrange systems represent many real-world systems including robots and vehicles, which must abide by safety-regulations, especially for use in human-occupied environments. These safety regulations include state constraints (position and velocity) and input constraints that must be respected at all times. ZCBFs are valuable for satisfying system constraints for general nonlinear systems, however their construction to satisfy state and input constraints is not straightforward. Furthermore, the existing barrier function methods do not address the multiple state constraints that are required for safety of Euler–Lagrange systems. In this paper, we propose a methodology to construct multiple, non-conflicting control barrier functions for Euler–Lagrange systems subject to input constraints to satisfy safety regulations, while concurrently taking into account robustness margins and sampling-time effects. The proposed approach consists of a sampled-data controller and an algorithm for barrier function construction to enforce safety (i.e. satisfy position and velocity constraints). The proposed method is validated in simulation on a 2-DOF planar manipulator. [ABSTRACT FROM AUTHOR]

In this paper, we study a distributed optimization problem using a subgradient projection algorithm for multi-agent systems subject to nonidentical constraints and communication delays under local communication. Here the agents capable of communicating with their local neighbors are constrained to remain in possibly different closed convex sets and optimize a global objective function composed of a sum of local objective functions, each of which is known to only one agent. First, we consider the case of fixed graphs and show that distributed optimization might not be achieved on general strongly connected directed graphs. Instead, the agents optimize a weighted sum of the local objective functions. Then we consider the case of switching graphs and show that distributed optimization can be achieved when the adjacency matrices are doubly stochastic and the union of the directed graphs is strongly connected among each time interval of a certain bounded length. Furthermore, we consider the case of communication delays, where the delays are mutually independent. It is shown that the distributed optimization problem can be solved by introducing additional delays to the subgradient projection algorithm and the communication delays can be arbitrarily bounded. Finally, numerical examples are included to show the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a solution method for parametric linear complementarity problems (PLCP) that relies on an enumeration technique to discover all feasible bases. The enumeration procedure is based on evaluating all possible combinations of active constraints and testing for feasibility. Although the enumeration approach is known to grow exponentially in the number of constraints, the formulation of the PLCP allows incorporation of cheap rank tests to quickly prune the infeasible directions in the exploration. The motivation for the development of the enumeration based PLCP solver is that it represents a direct method to solve parametric linear and quadratic optimization problems as well as their mixed-integer counterparts. These types of problems often arise in the field of model predictive control for linear and hybrid systems. The enumeration based PLCP solver offers another alternative to compute explicit solutions in the field of hybrid model predictive control that can be extremely effective in some important cases. [ABSTRACT FROM AUTHOR]

This paper considers a self-triggered MPC controller design strategy for tracking piecewise constant reference signals. The proposed triggering scheme is based on the relaxed dynamic programming inequality and the idea of reference governor; such a scheme computes both the updated control action and the next triggering time. The resulting self-triggered tracking MPC control law preserves stability and constraint satisfaction and also satisfies certain a priori chosen performance requirements without the need to impose stabilizing terminal conditions. An illustrative example shows the effectiveness of this self-triggered tracking MPC implementation. [ABSTRACT FROM AUTHOR]

Economic Model Predictive Control has recently gained popularity due to its ability to directly optimize a given performance criterion, while enforcing constraint satisfaction for nonlinear systems. Recent research has developed both numerical algorithms and stability analysis for the undiscounted case. The introduction of a discount factor in the cost, however, can be desirable in some cases of interest, e.g., economics, stochastically terminating processes, Markov decision processes, etc. Unfortunately, the stability theory in this case is still not fully developed. In this paper we propose a new dissipativity condition to prove asymptotic stability in the infinite horizon case and we connect our results with existing ones in the literature on discounted economic optimal control. Numerical examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper designs a model predictive control (MPC) law for constrained linear systems with stochastic additive disturbances and noisy measurements, minimising a discounted cost subject to a discounted expectation constraint. It is assumed that sensor data is lost with a known probability. Taking into account the data losses modelled by a Bernoulli process, we parameterise the predicted control policy as an affine function of future observations and obtain a convex linear-quadratic optimal control problem. Constraint satisfaction and a discounted cost bound are ensured without imposing bounds on the distributions of the disturbance and noise inputs. In addition, the average long-run undiscounted closed loop cost is shown to be finite if the discount factor takes appropriate values. We analyse robustness of the proposed control law with respect to possible uncertainties in the arrival probability of sensor data and we bound the impact of these uncertainties on constraint satisfaction and the discounted cost. Numerical simulations are provided to illustrate these results. [ABSTRACT FROM AUTHOR]

In this paper, we thoroughly investigate various aspects of economic model predictive control with average constraints, i.e., constraints on average values of state and input variables. In particular, we first show that a certain time-varying output constraint has to be included into the MPC problem formulation in order to ensure fulfillment of these average constraints. Optimizing a general (possibly economic) performance criterion may result in a non-converging behavior of the corresponding closed-loop system. While such a behavior might be acceptable in some cases, it may be undesirable for other types of applications. Hence as a second contribution, we provide a Lyapunov-like analysis to conclude that indeed asymptotic convergence to the optimal steady-state follows if the system satisfies a certain dissipativity condition. Finally, for the case that this dissipativity property is not satisfied but still a convergent behavior of the closed-loop is required, we examine two different methods how convergence can be enforced within an economic MPC setup by imposing additional average constraints on the system. In the first method, an additional average constraint is defined which results in the system being dissipative, while the second consists of imposing an additional even zero-moment average constraint. We illustrate our results with various examples. [ABSTRACT FROM AUTHOR]

In this paper, we show how heterogeneous bidirectional vehicle strings can be modelled as port-Hamiltonian systems. Analysis of stability and string stability within this framework is straightforward and leads to a better understanding of the underlying problem. Nonlinear local control and additional integral action is introduced to design a suitable control law guaranteeing l 2 string stability of the system with respect to bounded disturbances. [ABSTRACT FROM AUTHOR]

This paper presents almost sure convergence rates for system identification under binary, quantized, and regular sensors. To accommodate practical model complexity constraints, the system under consideration is represented by a modeled part together with an unknown-but-bounded unmodeled dynamics. Under uncorrelated noise sequences, identification errors with different sensor types are studied and tight error bounds are obtained without information or constraints on noise moment conditions. The results are then extended to correlated noise sequences whose remote past and distant future are asymptotically independent. In both cases, almost sure error bounds of the laws of iterated logarithms type are derived. [ABSTRACT FROM AUTHOR]

The fields of control and robotics are working toward the development of bipedal robots that can realize walking motions with the stability and agility of a human being. Dynamic models for bipeds are hybrid in nature. They contain both continuous and discrete elements, with switching events that are governed by a combination of unilateral constraints and impulse-like forces that occur at foot touchdown. Control laws for these machines must be hybrid as well. The goals of this paper are fourfold: highlight certain properties of the models which greatly influence the control law design; overview the literature; present two control design approaches in depth; and indicate some of the many open problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the global consensus problem for discrete-time multi-agent systems with input saturation constraints under fixed undirected topologies. We first give necessary conditions for achieving global consensus via a distributed protocol based on relative state measurements of the agent itself and its neighboring agents. We then focus on two special cases, where the agent model is either neutrally stable or a double integrator. For the neutrally stable case, any linear protocol of a particular form, which solves the consensus problem for the case without input saturation constraints, also solves the global consensus problem for the case with input saturation constraints. For the double integrator case, we show that a subset of linear protocols, which solve the consensus problem for the case without saturation constraints, also solve the global consensus problem for the case with input saturation constraints. The results are illustrated by numerical simulations. [Copyright &y& Elsevier]

Abstract: This paper presents a numerical solution for scalar state constrained optimal control problems. The algorithm rewrites the constrained optimal control problem as a sequence of unconstrained optimal control problems which can be solved recursively as a two point boundary value problem. The solution is obtained without quantization of the state and control space. The approach is applied to the power split control for hybrid vehicles for a predefined power and velocity trajectory and is compared with a Dynamic Programming solution. The computational time is at least one order of magnitude less than that for the Dynamic Programming algorithm for a superior accuracy. [Copyright &y& Elsevier]

Abstract: In this paper, an integral reinforcement learning (IRL) algorithm on an actor–critic structure is developed to learn online the solution to the Hamilton–Jacobi–Bellman equation for partially-unknown constrained-input systems. The technique of experience replay is used to update the critic weights to solve an IRL Bellman equation. This means, unlike existing reinforcement learning algorithms, recorded past experiences are used concurrently with current data for adaptation of the critic weights. It is shown that using this technique, instead of the traditional persistence of excitation condition which is often difficult or impossible to verify online, an easy-to-check condition on the richness of the recorded data is sufficient to guarantee convergence to a near-optimal control law. Stability of the proposed feedback control law is shown and the effectiveness of the proposed method is illustrated with simulation examples. [Copyright &y& Elsevier]

Abstract: The increasing interest in index in fault detection has led to some recent development in time domain investigation. This paper at first presents a necessary and sufficient condition of the index in finite time horizon for linear time-varying systems. It is shown that the feasibility of the index, which is given when the index is greater than a predefined value, is equivalent to the existence of a certain backward differential Riccati equation under a constraint. The square system as a special case is discussed. The corresponding results are extended to systems with unknown initial condition with a modified definition of the index. The condition for weighted index to emphasize the signal effect at different time instant is also derived by transformation. The result is also compared with the famous bounded real lemma. The connection with the linear time-invariant (LTI) case is also discussed. Finally, examples are given to illustrate the main results. [Copyright &y& Elsevier]

Abstract: This paper develops a cooperative, distributed form of MPC for linear systems subject to persistent, bounded disturbances. The distributed control agents make decisions locally and communicate plans with each other. Cooperation is promoted by consideration of a greater portion of the system-wide objective by each local agent; specifically, a local agent designs hypothetical plans for other agents, sacrificing local performance for the benefit of system-wide performance. These hypothetical plans are never communicated and no negotiation takes place. The method guarantees robust feasibility by permitting only one agent to optimize per time step, while ‘freezing’ the plans of others, and sufficient conditions are given for robust stability. These properties hold for all structures of cooperation between agents. Thus, a key feature is that coupled constraint satisfaction is compatible with inter-agent cooperation. [Copyright &y& Elsevier]

Abstract: This paper deals with a common practical problem where the output of a nonlinear sampled-data system is constrained to be measured at a relatively lower sampling rate. Designing a continuous-time controller that satisfies a specific dissipation inequality, it is shown that the closed-loop sampled-data system obtained by digital implementation of the emulated controller in a multirate scheme preserves similar dissipation inequality in a semiglobal practical sense. Moreover, we address multirate nonlinear control via an emulation method as an important application. [Copyright &y& Elsevier]

Abstract: Maintaining the connectivity of networked robots is a challenge in multirobot applications. In this paper, this challenging problem is addressed through the development of a novel controller that can guarantee that robots will approach their individual desired positions while maintaining existing network topology and avoiding obstacles. A new concept of connectivity constraint, along with a continuous modeling approach to obstacle avoidance, is utilized in building the navigation function. The designed potential field integrates the navigation requirement, connectivity constraint, and obstacle avoidance simultaneously, based on which a bounded control input is generated for multirobot control. It is shown that if the initial configurations of the robots are connected and the desired configuration is reachable, the proposed controller is capable of driving multirobots to their individual goal positions conditionally while keeping the underlying network connected. Simulations and experiments are finally performed using a group of mobile robots to demonstrate the effectiveness of the proposed controller. [Copyright &y& Elsevier]

Abstract: This paper presents a novel approach to design estimators for nonlinear systems. The approach is based on a combination of linear Moving Horizon Estimation (MHE) and Direct Virtual Sensor (DVS) techniques, and allows the design of estimators with guaranteed stability, which can account for convex constraints on the variables to be estimated. It is also shown that the designed estimators are optimal, in the sense that they give minimal worst-case estimation error, on the basis of the available finite number of noise-corrupted data, with respect to an ideal MHE filter (obtained by assuming exact knowledge of the system dynamics and of the global solution of the related nonlinear program). The approach is tested on a nonlinear mass–spring–damper system. [Copyright &y& Elsevier]

Abstract: The paper deals with the application of the so-called Reference (or Command) Governor constrained control strategy to the shape control of plasmas in thermonuclear fusion reactors with the main scope of optimizing tokamak operations also in conditions very close to the operating envelope limits. A primal inner loop controlling the plasma–wall distance is first designed; the Reference Governor device is then tuned to modify, whenever necessary, the reference signals to the inner loop, on the basis of constraints due to voltage saturations on the power supply converters, limitations of currents in the active control coils, minimum clearance between the plasma surface and the vacuum chamber wall, maximum induced magnetic fields and forces on coils. As usual in model predictive paradigms, the reference signal modification is accomplished through an on-line optimization procedure which embodies plasma model forecasts computed along a finite time virtual receding horizon. The ITER (International Thermonuclear Experimental Reactor) tokamak is assumed as the case study. Numerical simulations are carried out on a finite elements nonlinear model taking into account induced currents in the passive structures. The proposed application shows how almost a hundred constraints can be managed on-line by the Reference Governor. [Copyright &y& Elsevier]

Abstract: The paper considers a distributed robust estimation problem over a network with Markovian randomly varying topology. The objective is to deal with network variations locally, by switching observer gains at affected nodes only. We propose sufficient conditions which guarantee a suboptimal level of relative disagreement of estimates in such observer networks. When the status of the network is known globally, these sufficient conditions enable the network gains to be computed by solving certain LMIs. When the nodes are to rely on a locally available information about the network topology, additional rank constraints are used to condition the gains, given this information. The results are complemented by necessary conditions which relate properties of the interconnection graph Laplacian to the mean-square detectability of the plant through measurement and interconnection channels. [Copyright &y& Elsevier]

Abstract: This paper addresses the feedback control design for a class of nonholonomic systems which are subject to inequality state constraints defining a constrained (viability) set . Based on concepts from viability theory, the necessary conditions for selecting viable controls for a nonholonomic system are given, so that system trajectories starting in always remain in . Furthermore, a class of state feedback control solutions for nonholonomic systems are redesigned by means of switching control, so that system trajectories starting in converge to a goal set in , without ever leaving . The proposed approach can be applied in various problems, whose objective can be recast as controlling a nonholonomic system so that the resulting trajectories remain forever in a subset of the state space, until they converge into a goal (target) set in . The motion control for an underactuated marine vehicle in a constrained configuration set is treated as a case study; the set essentially describes the limited sensing area of a vision-based sensor system, and viable control laws which establish convergence to a goal set in are constructed. The robustness of the proposed control approach under a class of bounded external perturbations is also considered. The efficacy of the methodology is demonstrated through simulation results. [Copyright &y& Elsevier]

Abstract: The existing low gain feedback, which is a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero, has been designed in very specific ways. In this paper, by recognizing the and slow peaking phenomenon that exists in discrete-time systems under low gain feedback, more general notions of and norm vanishment are considered so as to provide a full characterization of the nonexistence of slow peaking phenomenon in some measured signals. Low gain feedback that does not lead to and slow peaking in the control input are respectively referred to as and low gain feedback. Based on the notions of and vanishment, not only can the existing low gain feedback be recognized as an low gain feedback, but also a new design approach referred to as the low gain feedback approach is developed for discrete-time linear systems. Parallel to the effectiveness of low gain feedback in magnitude constrained control, the low gain feedback is instrumental in the control of discrete-time systems with control energy constraints. The notions of and -vanishment also result in a systematic approach to the design of and low gain feedback by providing a family of solutions including those resulting from the existing design methods. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the problem of scheduling parallel Kalman filters for multiple processes, where each process is observed by a Kalman filter and at each time step only one Kalman filter could obtain observation due to practical constraints. To solve the problem, two novel notions, permissible consecutive observation loss (PCOL) and least consecutive observation (LCO), are introduced as criteria to describe feasible observation sequences for a process ensuring desired estimation qualities. Then two methods, namely, the threshold method and the periodic method, are proposed to calculate PCOL and LCO for each process. Based on the derived PCOL and LCO requirements, we develop two algorithms that are applicable to different situations: algorithm from the pinwheel problem for the case of and tree search algorithm for general cases. Also, to reduce the computational complexity of tree search algorithm, several useful pruning conditions are obtained. [Copyright &y& Elsevier]

Abstract: This paper is concerned with state and output feedback stabilization of a class of port-Hamiltonian systems with nonholonomic constraints. First we study canonical forms for port-Hamiltonian systems with nonholonomic constraints. Second, we give a new state feedback stabilization method by using non-smooth Hamiltonian functions via generalized canonical transformations. Third, we propose a dynamic output feedback stabilization method without measuring the velocity based on the corresponding state feedback result. Numerical examples demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: Identification of real-world systems is often applied in closed loop due to stability, performance or safety constraints. However, when considering Linear Parameter-Varying (LPV) systems, closed-loop identification is not well-established despite the recent advances in prediction error approaches. Building on the available results, the paper proposes the closed-loop generalization of a recently introduced instrumental variable scheme for the identification of LPV-IO models with a Box–Jenkins type of noise model structures. Estimation under closed-loop conditions with the proposed approach is analyzed from the stochastic point of view and the performance of the method is demonstrated through a representative simulation example. [Copyright &y& Elsevier]

Abstract: This paper discusses a method for estimating the covariance matrix of a multivariate stationary process generated as the output of a given linear filter fed by a stationary process . The estimated covariance matrix must satisfy two constraints: it must be positive semi-definite and it must be consistent with the fact that is the output of the given linear filter. It turns out that these constraints force the estimated covariance to lie in the intersection of a cone with a linear space. While imposing only the first of the two constraints is rather straightforward, guaranteeing that both are satisfied is a non-trivial issue to which quite a bit of attention has already been devoted in the literature. Our approach extends the method for estimating the Toeplitz covariance matrix of order of a process based on the biased spectral estimator (). This extension is based on the characterization of the output covariance matrix in terms of the filter parameters and the sequence of covariance lags of the input process. After introducing our estimation method, we propose a comparison performance between this one and other methods proposed in the literature. Simulation results show that our approach constitutes a valid estimation procedure. [Copyright &y& Elsevier]

Abstract: This paper derives performance limitations for disturbance rejection of scalar systems under information constraints subject to either bounded or Gaussian disturbances. Two kinds of disturbance are treated in a unified manner, using appropriate entropies and distortions. It is shown that the achievable performance cannot be improved even if the maximum information constraint is relaxed to an average information constraint. Another observation is that, while the information constraints are weaker than bit-rate or signal-to-noise ratio constraints on the communication channel, the same performance levels are achieved by the best encoder and decoder for disturbance rejection with the information constraints. [Copyright &y& Elsevier]

Abstract: In this paper, we study the stability of Networked Control Systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, packet dropouts and communication constraints. The transmission intervals and transmission delays are described by a sequence of continuous random variables. The complexity that the continuous character of these random variables introduces is overcome using a novel convex overapproximation technique that preserves the available probabilistic information. By focusing on linear plants and controllers, we present a modelling framework for NCSs based on discrete-time linear switched and parameter-varying systems. Stability (in the mean-square) of these systems is analysed using a new stochastic computational technique, resulting in a finite number of linear matrix inequalities. We illustrate the developed theory on the benchmark example of a batch reactor. [Copyright &y& Elsevier]

Abstract: This paper proposes an explicit solution to the model predictive control of linear systems subject to non-convex polyhedral constraints. These constraints are modeled as the union of a finite number of convex polyhedra. The algorithm is based on calculating the explicit solution to a modified problem with linear constraints defined as the convex hull of the original ones and classifying its regions by their relation with the regions of the explicit solution to the original problem. Some of the regions are divided, and a procedure based on sum-of-squares programming is designed to determine which of the possible solutions are in fact optimal. Finally, the online algorithm is shown to be better in terms of computational cost and memory requirements than an algorithm based on obtaining and comparing the solutions of the problem using as constraints the polyhedra whose union forms the non-convex regions, both theoretically and by the results of an example. [Copyright &y& Elsevier]