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This paper investigates the stability issues of model predictive control (MPC) for discrete-time linear systems with state and finite control set (FCS) constraints subject to time-varying disturbances. A new FCS-MPC design and analysis framework is developed using the disturbance estimation approaches and the tool of robust positive invariant (RPI) set sequence. It encompasses a discrete-time exogenous signal observer that helps characterize the estimated dynamics within well-defined bounds and a quantized control law that adheres to both state and input constraints. The practical asymptotical stability of the resulting closed-loop system is shown to be guaranteed, and the tracking error remains uniformly bounded. Finally, simulation results of a numerical example validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the robust asymptotic stabilization of a linear time-invariant (LTI) system by static feedback with a static state quantization. It is shown that the controllable LTI system can be stabilized to zero in a finite time by means of nonlinear feedback with a quantizer having a limited (finite) number of values (quantization seeds) even when all parameters of the controller and the quantizer are time-invariant. The control design is based on generalized homogeneity. A homogeneous spherical quantizer is introduced. The static homogeneous feedback is shown to be a local (or global) finite-time stabilizer for any controllable linear system (depending on the system matrix). The tuning rules for both the quantizer and the feedback law are obtained in the form of Linear Matrix Inequalities (LMIs). The closed-loop system is proven to be robust with respect to some bounded matched or vanishing mismatched perturbations. Theoretical results are supported by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies the rendezvous problem for a second-order multi-agent system on the hyperboloid under a proximity-based communication topology. Using the Riemannian geometrical structure on the hyperboloid, we design a nonlinear feedback control law in which each agent has a limited sensing range. By analyzing the switching behavior of the communication topology, we show that the switching time of the resulting closed-loop system is finite, and the connectivity of the communication topology is preserved if the initial network is connected. In addition, we also provide an analysis of the asymptotic behavior of the second-order closed-loop system on the hyperboloid and prove that the proposed feedback control law enables all agents to converge to the same position. [ABSTRACT FROM AUTHOR]

We propose a novel adaptive learning-based model predictive control (MPC) scheme for interconnected systems which can be decomposed into several smaller dynamically coupled subsystems with uncertain coupling. The proposed scheme is mainly divided into two main online phases; a learning phase and an adaptation phase. Set membership identification is used in the learning phase to learn an uncertainty set that contains the coupling strength using online data. In the adaptation phase, rigid tube-based robust MPC is used to compute the optimal predicted states and inputs. Besides computing the optimal trajectories, the MPC ingredients are adapted in the adaptation phase taking the learnt uncertainty set into account. These MPC ingredients include the prestabilizing controller, the rigid tube, the tightened constraints and the terminal ingredients. The recursive feasibility of the proposed scheme as well as the stability of the corresponding closed-loop system are discussed. The developed scheme is compared in simulations to existing schemes including robust, adaptive and learning-based MPC. [ABSTRACT FROM AUTHOR]

This paper concerns the fixed-time control with an arbitrarily prescribed upper bound of settling-time (UBST) for nonlinear systems with asymmetric output constraints. We introduce a novel time-varying gain function that effectively addresses the issue of infinite-gain, which has been a challenge in related research. By utilizing this gain function, we present two theorems that employ the Lyapunov function for constrained nonlinear systems. These theorems serve as guidelines for constructing controllers without violation of constraints. In addition, a novel barrier Lyapunov function (BLF) is exploited which is equivalent to the classical one for nonlinear systems without constraints. By using the proposed theorems, BLF and fixed-time backstepping design procedure, a state-feedback controller is constructed and analyzed for output-constrained nonlinear systems. It is proved that the designed controller can render the closed-loop system converges to the origin within a fixed settling time while maintaining at the origin thereafter, the controller is uniformly bounded and the output constraints are not violated. Finally, simulations and comparisons are provided to verify the proposed control schemes. [ABSTRACT FROM AUTHOR]

Motivated by the linearized model of unstable burning in solid propellant rockets, this article addresses the adaptive event-triggered output feedback control of uncertain parabolic PDEs. First, we construct an adaptive identifier that consists of a gradient estimator, and then design a continuous-in-time controller. On this basis, we design a novel event-triggered output feedback controller and construct dynamic triggering conditions to assure the global asymptotic stability of the closed-loop system around the limit points. Furthermore, the parameter estimation is proven to converge to the true value when an additional constant input at the boundary is applied to the closed-loop system. Finally, simulation data verifies the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The present paper is devoted to sampled-data control design of a PDE–PDE cascade system. These PDEs are governed by heat equations with different reaction coefficients. In order to stabilize the cascaded heat–heat system, we start with the design of continuous-time feedback control law. Then sampled-data control is further proposed for practical reasons. Sufficient conditions are derived for guaranteeing the exponential stability and well-posedness of the corresponding closed-loop system via Lyapunov method and modal decomposition method. Numerical examples illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, finite-time stabilization is investigated for a class of non-local Lipschitzian large-scale stochastic nonlinear systems with two types of uncertainties, including parametric uncertainties and uncertain interactions. First, we present a new stochastic finite-time stability theorem on stochastic adaptive finite-time control, by which we obtain an existing finite-time stability result for the interconnected stochastic nonlinear systems. Then, for a class of large-scale stochastic nonlinear systems with uncertainties, an adaptive finite-time controller is constructively designed. It is proved by the developed finite-time stability theorem that there exists a global weak solution to the closed-loop system, the trivial weak solution of the closed-loop system is globally stable in probability and the states of the system almost surely converge to the origin in finite time. At last, a simulation example is given to show the effectiveness of the proposed design procedure. [ABSTRACT FROM AUTHOR]

This paper presents a switching control strategy as a criterion for policy selection in stochastic Dynamic Programming problems over an infinite time horizon. In particular, the Bellman operator, applied iteratively to solve such problems, is generalized to the case of stochastic policies, and formulated as a discrete-time switched affine system. Then, a Lyapunov-based policy selection strategy is designed to ensure the practical convergence of the resulting closed-loop system trajectories towards an appropriately chosen reference value function. This way, it is possible to verify how the chosen reference value function can be approached by using a stabilizing switching signal, the latter defined on a given finite set of stationary stochastic policies. Finally, the presented method is applied to the Value Iteration algorithm, and an illustrative example of a recycling robot is provided to demonstrate its effectiveness in terms of convergence performance. [ABSTRACT FROM AUTHOR]

This paper addresses a nonsmooth aggregative game to control multiple noncooperative players, each with a nonsmooth cost function that depends not only on its own decision but also on some aggregate effect among all the agents. In addition, the decision of each player is restricted by private and coupling constraints. To address these concerns, a distributed generalized Nash equilibrium (GNE) seeking algorithm is proposed. Two features distinguish our methods from the existing GNE seeking algorithms. Firstly, an adaptive penalty method is introduced to drive each player's action to enter the set of private constraints. The adaptive term ensures automatic adjustment of penalty parameter based on the degree of constraint violation excluding any prior calculation. Secondly, a distributed dynamic event-triggered mechanism is designed for each player to lessen communication energy. In comparison to the static event-triggered mechanism, the proposed dynamic mechanism possesses larger inter-execution time intervals. As the discontinuity of the event-triggered mechanism can impact the existence of a solution to the closed-loop system in the classical sense, we adapt a nonsmooth analysis technique, including differential inclusion and Filippov solution. Through nonsmooth Lyapunov analysis, the convergence result and the avoidance of Zeno behavior are established. Finally, two engineering examples are provided to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper revisits a classical adaptive control problem: adaptive state tracking control of a state-space plant model, and solves the open discrete-time state tracking model reference adaptive control problem. Adaptive state tracking control schemes for continuous-time systems have been reported in the literature, using a Lyapunov-algorithm based design and analysis procedure. Such a procedure has not been successfully applied to the discrete-time adaptive state tracking control problem which has remained open. In this paper, new adaptive state tracking control schemes are developed for discrete-time systems, using gradient algorithms for updating the controller parameters. Both direct and indirect adaptive designs are derived, which have the desired parameter adaptation properties and closed-loop system stability and state tracking properties. Such a new gradient-algorithm based framework is also applicable to the continuous-time adaptive state tracking control problem to develop new solutions, as compared with the traditional Lyapunov-algorithm based solutions. [ABSTRACT FROM AUTHOR]

In this paper, the resilient control for switched systems in the presence of deception attack and denial-of-service (DoS) attack is addressed. Due to the interaction of two kinds of attacks and the asynchronous phenomenon of controller mode and subsystem mode, the system dynamics becomes much more complex. A criterion is derived to ensure the mean square security level of the closed-loop system. This in turn reveals the balance of system resilience and control performance. Furthermore, a mixed-switching control strategy is put forward to make the system globally asymptotically stable. It is shown that the system will still converge to the equilibrium even if the deception attack occurs. Finally, simulations are carried out to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to synthesize positive invariant sets for unmodeled nonlinear systems using direct data-driven techniques. The data-driven invariant sets are used to design a data-driven command governor that selects a command for the closed-loop system to enforce constraints. Using basis functions, we solve a semi-definite program to learn a sum-of-squares Lyapunov-like function whose unity level-set is a constraint admissible positive invariant set, which determines the constraint admissible states and input commands. Leveraging Lipschitz properties of the system, we prove that tightening the model-based design ensures robustness of the invariant set to the inherent plant uncertainty in a data-driven framework. To mitigate the curse-of-dimensionality, we repose the semi-definite program into a linear program. We validate our approach through two examples: First, we present an illustrative example where we can analytically compute the maximum positive invariant set and compare with the presented data-driven invariant set. Second, we present a practical autonomous driving scenario to demonstrate the utility of the presented method for nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example. [ABSTRACT FROM AUTHOR]

We study the problem of seeking the source of a scalar signal with a force- and torque-controlled unicycle. The vehicle does not have the capability to measure or track its position. The only information about the vehicle's position relative to the source is given by measurements of the signal. We propose a feedback law that induces a uniform forward motion and an almost uniform rotational motion. This in turn leads to an almost circular motion of the unicycle; i.e., a motion along the boundary of a disk. An application of the divergence theorem reveals that the measurements of the signal along the boundary of the disk provide access to the gradient of an averaged signal, where the average is taken over the entire disk. Such a local average of the sensed signal can eliminate undesired local extrema, which in turn is beneficial for the goal of reaching a global extremum. We prove practical asymptotic stability for the closed-loop system with respect to extrema of the averaged signal. Our theoretical analysis takes L ∞ -measurement errors of the signal into account. We compare the performance of the proposed control law to another source seeking method in the presence of local extrema through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction–diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The stabilization problem under consideration involves random perturbations modeled by a finite-state Markov process that further obstruct the actuation path at the controlled boundary of the infinite-dimension plant. This scenario is useful to describe several actuation failure modes in process control. Employing the recently introduced infinite-dimensional representation of the state of an actuator subject to stochastic input delay for ODEs (Ordinary Differential Equations), we convert the stochastic input delay into r + 1 unidirectional advection PDEs, where r corresponds to the number of jump states. Our stability analysis assumes full-state measurement of the spatially distributed plant's state and relies on a hyperbolic–parabolic PDE-PDE cascade representation of the plant plus actuator dynamics. Integrating the plant and the nominal stabilizing boundary control action, all while considering probabilistic delay disturbances, we establish the proof of mean-square exponential stability as well as the well-posedness of the closed-loop system when random phenomena weaken the nominal actuator compensating effect. Our proof is based on the Lyapunov method, the theory of infinitesimal operator for stability, and C 0 -semigroup theory for well-posedness. Our stability result refers to the L 2 -norm of the plant state and the H 2 -norm of the actuator state. Furthermore, our study presents a qualitative analysis of the maximum deviation of the stochastic disturbance relative to the nominal delay, which is expressed as a function of the severity of the plant instability, namely, the magnitude of the reactivity coefficient and the known upper bound of the transition rate of the underlying stochastic perturbations. Extensive simulation results illustrate the viability of the robustness study. [ABSTRACT FROM AUTHOR]

This paper studies negative imaginariness and the static output feedback H ∞ control synthesis of descriptor systems based on the state–space symmetric model. First, under the assumption that the transfer function matrix is proper, necessary and sufficient conditions to determine negative imaginary properties are established for descriptor systems with state–space symmetry. Then, based on state–space symmetry, a sufficient condition is derived for the design of static output feedback controller, such that the resulting closed-loop system satisfies negative imaginary and H ∞ performance. Finally, two circuit networks and a numerical example are provided to validate the main results of the paper. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of adaptive practical fixed-time synchronized tracking control of autonomous surface vehicle (ASV) systems with model uncertainties and external disturbances. In order to force the tracking error to a required range, a piecewise continuous finite-time prescribed performance function (FTPPF) is employed. A sliding mode controller incorporating FTPPF is built based on the norm-normalized (NN) sign function to simultaneously follow the desired trajectory. A set of adaptive laws is proposed to estimate model uncertainties and external disturbances with the constructed sliding mode surface. Then, an adaptive sliding mode controller is designed to achieve prescribed dynamic convergence performance and tracking accuracy. Mathematically, the practical fixed-time stability of ASV systems is firmly proven and all the signals in the closed-loop system are bounded. Finally, simulations are performed utilizing Matlab/Simulink to show the availability of the acquired algorithm. [ABSTRACT FROM AUTHOR]

Model-based control strategy is introduced for improving the closed-loop performance of switched systems under network communication in this paper. In traditional networked control system, a Zero-Order Hold (ZOH) is often used at the controller side to realize continuous feedback control. However, to use a ZOH usually decreases control accuracy since the state will be held invariably during each sampling period. In order to improve control accuracy, we introduce a model-based control strategy instead of ZOH-based one and propose two analysis frameworks for switched linear systems in network communication environment with periodic sampling mechanism (PSM) and event-triggered sampling mechanism (ETSM), respectively. A model-based dynamic switching controller is set up with certain robust performance. Asynchronous switching is taken into account since the switching time sequence of the controller is determined by the network transmission time sequence which cannot coincide with the controlled system. Under switching and control gain conditions, stability criteria of the closed-loop switched system in network communication environment are derived and verified through two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the tracking control issue for a kind of state-constrained nonlinear cyber–physical systems (CPSs) with exogenous interferences, which are subject to deception attacks started in controller–actuator (C–A) channel. Firstly, we design a nonlinear state dependent function (NSDF) which only relies on the restricted states to deal with the asymmetric state constraints. Furthermore, introducing a coordinate transformation and integrating it into each step of dynamic surface control (DSC) based backstepping method, we wholly evade the feasibility condition forced on the virtual control signals. As a result, a novel adaptive tracking control scheme is developed, which is capable of settling exogenous disturbances and deception attacks concurrently. Especially, the proposed control architecture can not only make sure that all the tracking errors converge into a pre-defined small region of the equilibrium point, but also guarantee that the total signals of the closed loop system conform to the corresponding state restrictions. Eventually, the benefits and superiority of the proposed control framework are theoretically authenticated and practically illustrated through a representative example. [ABSTRACT FROM AUTHOR]

Most research on control of nonlinear systems using backstepping concentrates on construction of feedback controllers to achieve stability and/or steady-state tracking performance. Little research considers systematic methods for tuning nonlinear feedback controllers to guarantee the transient performance. This paper investigates how parameters of a backstepping controller can be determined to achieve the predefined settling time and overshoot, which are basic criteria for the transient performance. First, some modifications are made for the backstepping design method by introducing more parameters so that there are more degrees of freedom for parameter tuning. Second, the pole-placement method is used for the linear part of the closed-loop system corresponding to a backstepping controller. Third, an objective function is defined by summing the square of errors between the corresponding coefficients of the desired and real characteristic polynomials. Fourth, constraints are introduced to guarantee the negative semi-definiteness of the time derivative of the Lyapunov function. Fifth, the controller parameters can be found by minimizing the objective function. Finally, simulation and experimental results show that, compared with the existing method, the proposed method is more effective and efficient for fine tuning backstepping controllers. [ABSTRACT FROM AUTHOR]

This research focuses on the input delay tolerance problem for C 0 yet possibly non-locally Lipschitz continuous nonlinear systems that are not locally exponentially stabilizable (LES) by any smooth feedback. Using the Lyapunov–Razumikhin method, nonsmooth analysis/synthesis tools and homogeneity with respect to a family of dilations, we show that global asymptotic stabilizability (GAS) by nonsmooth homogeneous state feedback implies semiglobal asymptotic stability (SGAS) of the closed-loop system with input delay — the property of semiglobal input delay tolerance (SGIDT), if the C 0 nonlinear systems are homogeneous with positive degree. In the case of output feedback, we prove that the SGIDT property still holds for the same class of nonlinear systems if they are GAS by homogeneous output feedback. As a byproduct of these developments, new SGIDT results under nonsmooth feedback are obtained for significant classes of inherently nonlinear systems with actuator delay. [ABSTRACT FROM AUTHOR]

A time-varying state feedback is presented that guarantees stability and a hyperexponential rate of convergence of all trajectories to the origin for a chain of integrators. It is shown that this convergence property is uniform with respect to matched bounded external disturbances. An implicit time-discretization scheme of the closed-loop system is given, which preserves all main properties of the continuous-time counterpart, and in addition has bounded errors with respect to the measurement noises. Based on this discretization, for sampled-and-hold implementation, a modified linear time-varying state feedback is proposed, which provides an accelerated rate of convergence to the continuous-time plant. The efficiency of the suggested control algorithms is illustrated through numeric experiments. [ABSTRACT FROM AUTHOR]

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]

In this paper, we extend a newly developed time-delay approach of extremum seeking (ES) from quadratic maps to general nonlinear maps, which substantially expands the scope of application of the time-delay method. The gradient-based ES in the case of single-variable and multi-variable nonlinear static maps are considered. Different from the recent literature, the time-delay method in this paper is applicable to a big family of nonlinear maps satisfying a couple of mild assumptions. By transforming the original ES system into a kind of time-delay system of neutral type, and further transforming the neutral delay differential equation into the perturbed ordinary differential equation (ODE), we provide simple inequalities that guarantee practical stability of the ES closed-loop system. With a prior knowledge about the upper bounds of the nonlinear map and its gradient and Hessian, the time-delay approach suggests a quantitative calculation on the lower bound of dither frequency and the ultimate upper bound of estimation error, which is difficult to achieve by the classical averaging method. [ABSTRACT FROM AUTHOR]

Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results. [ABSTRACT FROM AUTHOR]

This work investigates the adaptive optimal tracking control problem for networked discrete-time linear systems by directly using the data transmitted via communication networks. It is shown that the concerned problem can be addressed by solving two sub-problems: an adaptive optimal control one and an adaptive output regulation one. Two novel online reinforcement learning based policy iteration and value iteration algorithms are developed, which constitute an integrated framework to learn the optimal feedback control gain and the solutions to regulator equations by directly using the data transmitted via communication networks. Furthermore, it is shown that the tracking error of the closed-loop control system is mean square asymptotically stable even in the case of network packet stochastic dropouts. Simulation results demonstrate the efficacy of the proposed approaches. [ABSTRACT FROM AUTHOR]

We consider the problem of achieving prescribed performance metrics on the output tracking error, for uncertain strict-feedback systems, while satisfying inelastic control input constraints in the form of magnitude saturation. Inspired by the prescribed performance control (PPC) methodology, we propose a switching control strategy comprised of two operational units: a traditional PPC and a Safety Controller. The former enforces the output error to evolve strictly inside a user-defined performance envelope that incorporates all the desired performance characteristics. However, in the presence of input saturation this envelope can be easily violated, leading to PPC instability. On the other hand, the Safety Controller enables the safe escaping, thus avoiding the appearance of this internal instability phenomenon. We prove that the closed-loop system solution is complete and non-zeno. Furthermore, we show that the tracking error evolves inside a modified performance envelope, guaranteeing a prescribed minimum convergence rate and a controlled maximum steady-state error. Simulation studies clarify and verify the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper proposes a new output feedback model reference adaptive control (MRAC) method for discrete-time linear time-invariant systems with arbitrary relative degrees. The proposed method does not require any prior knowledge of the high-frequency gain represented by k p , thereby completely eliminating the common design condition in the traditional discrete-time MRAC framework: the sign of k p is known, as well as an upper bound on | k p |. Specifically, an output feedback adaptive control law is developed, which incorporates a time-varying gain function to effectively address the singularity issue. The developed adaptive control law leads to the derivation of a linear estimation error equation for the closed-loop system. Consequently, a gradient algorithm based parameter update law is directly formulated by utilizing the estimation error and some other available signals without requiring any prior knowledge of k p. In comparison to the traditional MRAC and Nussbaum function-based methods, it does not necessitate any additional design conditions or involve any transient performance issues, while still ensuring closed-loop stability and asymptotic output tracking for any given bounded reference signal. The simulation study showcases the design procedure and evaluates the efficacy of the proposed control method. [ABSTRACT FROM AUTHOR]

Recently, a constructive method was suggested for finite-dimensional observer-based control of 1D linear heat equation, which is robust to input/output delays. In this paper, we aim to extend this method to the 2D case with general time-varying input/output delays or sawtooth delays (that correspond to network-based control). We use the modal decomposition approach and consider boundary or non-local sensing together with non-local actuation, or Neumann actuation with non-local sensing. To compensate the output delay that appears in the infinite-dimensional part of the closed-loop system, for the first time for delayed PDEs we suggest a vector Lyapunov functional combined with the recently introduced vector Halanay inequality. We provide linear matrix inequality (LMI) conditions for finding the observer dimension and upper bounds on delays that preserve the exponential stability. We prove that the LMIs are always feasible for large enough observer dimension and small enough upper bounds on delays. A numerical example demonstrates the efficiency of our method and shows that the employment of vector Halanay's inequality allows for larger delays than the classical scalar Halanay inequality for comparatively large observer dimension. [ABSTRACT FROM AUTHOR]

A resource-aware fault tolerant control (RA-FTC) issue is considered in this work for Markovian jump systems (MJS) via a self-triggered scheme. First, based on uncertain polytopic theory and system augmentation technique, a sliding mode observer is designed to reconstruct faults and states via the self-triggered nonuniform sampled outputs. Second, a self-triggered fault tolerant controller (ST-FTC) is constructed based upon the reconstructed fault and state signals. Then, the desired performance of the overall closed-loop system can be achieved. Third, with the aid of Lyapunov theorem and linear matrix inequality technique, the stochastically stabilization can be guaranteed under the action of the proposed ST-FTC. It is worthy noting that the self-triggered mechanism is firstly introduced for FTC of MJSs to reduce the computation resources. Finally, two examples are provided to show the effectiveness of the investigated RA-FTC scheme. [ABSTRACT FROM AUTHOR]

In this paper, we consider the stabilization of an axially moving Kirchhoff-type beam with rotational inertia under controls of force and torque at one boundary. The proposed negative feedbacks of the transverse velocity and angular velocity applied at the control end cover a large class of nonlinear feedback functions. The well-posedness of the resulting closed-loop system is established by means of the nonlinear semigroup theory, where the solution is shown to be depending continuously on the initial value. The asymptotic stability of the closed-loop system is guaranteed by resolving a dissipative ordinary differential equation. The decay rates of the vibration for some special nonlinear feedback functions can be estimated by the dissipative ordinary differential equation provided that growth restrictions on these nonlinear feedbacks near the origin are required. Three types of examples including exponential, polynomial and polynomial-logarithmic decay forms are deduced, and the numerical simulations are presented to verify the proposed control approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose decentralized prescribed-time control schemes for a class of interconnected nonlinear systems by using time-varying high-gain domination approach. It is shown that prescribed-time exact regulation can be achieved by a linear observer based controller in the presence of completely unknown interactions. Besides, without significantly modifying the original controller structure, we develop a singularity-free controller with bounded time-varying feedback to drive the system state to converge to a compact set within a preset time, and ultimately converge to zero. In both of these approaches, the controller and observer designs have a dual architecture, thereby obviating the need for the separation principle (which might not be valid for nonlinear systems with mismatched uncertainties). In addition, the relationship between the upper bound of the time-varying gain and the stability of the closed-loop system is thoroughly analyzed. [ABSTRACT FROM AUTHOR]

In this paper, the stabilization problem of nonlinear time-delay systems in presence of known exogenous disturbances and by means of quantized sampled-data event-based controllers is investigated. In particular, nonlinear systems with state delays are studied. Known exogenous disturbances affecting the plant dynamics are considered in order to address, for instance, tracking control problems commonly studied by considering the stabilization problem of the corresponding tracking error system in which the chosen reference signal appears as a known exogenous signal. The stabilization in the sample-and-hold sense theory is used as a tool to provide sufficient conditions for the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the quantized sampled-data implementation of continuous-time controllers, updated through a proposed event-based mechanism, guarantees the semi-global practical stability property, with arbitrarily small final target ball of the origin, of the related closed-loop system. A spline approximation methodology is used in order to: (i) cope with the problem of the possible non-availability in the buffer of suitable past values of the system variables needed for the digital implementation of the controller; (ii) consider approximations related to the hardware implementation of the signal describing the known exogenous disturbance (e.g., the chosen reference signal). The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results, one of which concerning a single-link flexible joint robot arm with time delays. [ABSTRACT FROM AUTHOR]

Recently, a Lyapunov design of least-squares model-reference adaptive control (LS-MRAC) has been proposed. Unlike other least-squares based algorithms, the update law is driven only by the tracking error and, in this way, it does not require normalization or parameter projection to assure stability of the closed-loop system. Moreover, the algorithm has striking improved tracking error transient and superior parameter convergence properties when compared with a conventional MRAC. Also recently, a new design employing high-order parameter tuners has been proposed. In this design, the parameter derivatives are quite easily and systematically obtained. A key point of the procedure is the Lyapunov function used for the analysis that explicitly considers the derivatives of the parameter. The implementation of the algorithm requires finding a symmetric positive definite matrix such that a Schur complement is negative definite. This is a fundamental property to assure its stability. The solution to this problem leads to a novel simple proof for the equivalence between the Routh–Hurwitz stability criterion and the Lyapunov's method. In this work both design methodologies are combined, that is, the LS-MRAC algorithm is redesigned with high-order tuners. [ABSTRACT FROM AUTHOR]

The problem of bearing-based formation control with disturbance rejection has been studied by quite a few papers under various assumptions on the disturbances such as constant disturbances, trigonometric polynomial disturbances or bounded uniformly continuous disturbances with known bounds. In this paper, we further study the same problem with the disturbances being bounded piecewise continuous time functions. We first consider the case where the bounds of the disturbances are known. We show that the problem can be solved by a distributed static state feedback control law. Then we further consider the case where the bounds of the disturbances are unknown. We manage to solve this problem by introducing the adaptive control technique to deal with the unknown bounds of the disturbances. Our results include all the existing results on the bearing-based formation control with disturbance rejection as special cases. Moreover, we present a sufficient condition on the initial values of the closed-loop system for each case that prevents the collision. [ABSTRACT FROM AUTHOR]

This paper proposes a constructive solution to the output regulation — output tracking problem for a general class of interconnected systems. The class of systems under consideration consists of a linear 2 × 2 hyperbolic Partial Differential Equations (PDE) system coupled at both ends with Ordinary Differential Equations (ODEs). The proximal ODE system, which represents actuator dynamics, is actuated. Colocated measurements are available. The distal ODE system represents the load dynamics. The control objective is to ensure, in the presence of a disturbance signal (regulation problem), that a virtual output exponentially converges to zero. By doing so, we can ensure that a state component of the distal ODE state robustly converges towards a known reference trajectory (output tracking problem) even in the presence of a disturbance with a known structure. The proposed approach combines the backstepping methodology and frequency analysis techniques. We first map the original system to a simpler target system using an invertible integral change of coordinates. From there, we design an adequate full-state feedback controller in the frequency domain. Following a similar approach, we propose a state observer that estimates the state and reconstructs the disturbance from the available measurement. Combining the full-state feedback controller with the state estimation results in a dynamic output-feedback control law. Finally, existing filtering techniques guarantee the closed-loop system robustness properties. [ABSTRACT FROM AUTHOR]

This paper presents a model predictive control (MPC) approach for a class of asynchronously switched linear systems with mode-dependent dwell time (MDT). Asynchronous switching which refers to the mismatch between system modes and desired mode-dependent controllers may result in infeasibility of the conventional switched MPC design or even make the closed-loop system unstable. To handle this problem, the concept of stage MDT is employed and its minimum admissible value is determined offline so as to ensure the reachable set of a starting region is included in a target region. Then, we compute a constraint admissible contractive asynchronous switching MDT invariant (AMI) set as the common terminal constraints for all the switching modes and find out an important property: The existence of such an AMI set is equivalent to the asymptotic stability of the asynchronously switched closed-loop system. By letting the reachable set be contained in the AMI set, we present two criteria to determine the minimum admissible stage MDT offline such that the closed-loop system is asymptotically stable. Finally, a numerical example is given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the adaptive control of robot manipulators with closed architecture and parametric uncertainty. We propose a new class of adaptive controllers via exploiting the potential as applying the forwardstepping approach and the input–output properties of an inverted form of the dynamics of robots with closed architecture. The condition that ensures the stability and convergence of the closed-loop system becomes rather moderate due to the new design and analysis, and the result presented further enhances the connection between nonlinear control theory and most industrial/commercial robotic applications. [ABSTRACT FROM AUTHOR]

This paper investigates the formation of fixed-wing UAVs in 3D, which communicate via a directed acyclic graph. Different from common formation problems, we consider the roto-translation invariant (RTI) formation, where the "roto-translation" refers to a rigid-body motion obtained by composing rotation and translation. Besides, the fixed-wing UAV is modeled by a 3-D nonholonomic constrained rigid body instead of a particle agent. The main results of this paper include proposing the formation feasibility conditions and designing the formation controller. Firstly, we define the RTI formation and propose the conditions to guarantee that the formations are feasible for the fixed-wing UAVs under the nonholonomic and input saturation constraints. Secondly, given feasible formations, we design a formation controller by introducing a virtual leader and employing the compensation of rotation, followed by proving the stability of the closed-loop system. Finally, simulation examples are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization of an uncertain wave equation which describes the vibration dynamics of a flexible string. All the system parameters are unknown while the disturbance with unknown bound and period is allowed which lead to more serious uncertainties than the related literature, and hence result into the incapability of the traditional schemes. To solve the control problem, a novel condition-based adaptive control framework is developed in the paper. Specifically, as preparation for the adaptive control design, a state-feedback controller is first designed under the assumption that all the system parameters are known. Then, an adaptive controller, together with two continuous adaptive laws and a condition-based updating mechanism for the online tuning of the controller parameters, is proposed for the original uncertain system. Finally, it is proven that the updating of controller parameters under the proposed condition-based updating mechanism stops at a finite time instant, then the proposed controller guarantees the stability of the resulting closed-loop system. The proposed theoretical results are validated by a simulation example. [ABSTRACT FROM AUTHOR]

An in-domain finite dimensional controller for a class of distributed parameter systems on a one-dimensional spatial domain formulated under the port-Hamiltonian framework is presented. Based on (Trenchant et al. 2017) where positive feedback and a late lumping approach is used, we extend the Control by Interconnection method and propose a new energy shaping methodology with an early lumping approach on the distributed spatial domain of the system. Our two main control objectives are to stabilize the closed-loop system, as well as to improve the closed-loop dynamic performances. With the early lumping approach, we investigate two cases of the controller design, the ideal case where each distributed controller acts independently on the spatial domain (fully-actuated), and the more realistic case where the control action is piecewise constant over certain intervals (under-actuated). We then analyze the asymptotic stability of the closed-loop system when the infinite dimensional plant system is connected with the finite dimensional controller. Furthermore we provide simulation results comparing the performance of the fully-actuated case and the under-actuated case with an example of an elastic vibrating string. [ABSTRACT FROM AUTHOR]

Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its computation is sometimes prohibitive. This paper introduces an approach combining the two methodologies to overcome their individual limitations. The predictive control law for constrained linear quadratic regulation (CLQR) problems has been proven to be piecewise affine (PWA) while the value function is piecewise quadratic. We exploit these formal results from MPC to design an ADP method for CLQR problems with a known model. A novel convex and piecewise quadratic neural network with a local–global architecture is proposed to provide an accurate approximation of the value function, which is used as the cost-to-go function in the online dynamic programming problem. An efficient decomposition algorithm is developed to generate the control policy and speed up the online computation. Rigorous stability analysis of the closed-loop system is conducted for the proposed control scheme under the condition that a good approximation of the value function is achieved. Comparative simulations are carried out to demonstrate the potential of the proposed method in terms of online computation and optimality. [ABSTRACT FROM AUTHOR]

In this paper, we propose the twisting observer for robustly estimating the states of a second-order uncertain system. It is well-known that the twisting algorithm achieves the second-order sliding mode condition using the sign information of both the plant states. When all the states are not available, the twisting algorithm cannot be extended to the estimation problem directly. Hence, our proposed observer approximates this unknown sign term for the non-measurable state in the twisting observer with a delayed output-based switching function. It is shown that under some suitable gain conditions, the observer can guarantee any arbitrary accuracy of estimation error for some appropriate delay parameter which can be varied online. The advantage of this observer is that one needs to control only the delay parameter to achieve the desired steady-state accuracy, unlike the additional nonlinear functions found in the existing observers. The application of this observer to output feedback stabilization is also discussed. The separation principle for the closed-loop system is shown by designing the gains of controller and observer independently. Finally, we illustrate the design and performance of the proposed state observation scheme through a numerical example. [ABSTRACT FROM AUTHOR]

We propose a hybrid control algorithm that guarantees fast convergence and uniform global asymptotic stability of the unique minimizer of a C 1 , convex objective function. The algorithm, developed using hybrid system tools, employs a uniting control strategy, in which Nesterov's accelerated gradient descent is used "globally" and the heavy ball method is used "locally", relative to the minimizer. Without knowledge of its location, the proposed hybrid control strategy switches between these accelerated methods to ensure convergence to the minimizer without oscillations, with a (hybrid) convergence rate that preserves the convergence rates of the individual optimization algorithms. We analyze key properties of the resulting closed-loop system including existence of solutions, uniform global asymptotic stability, and convergence rate. Additionally, stability properties of Nesterov's method are analyzed, and extensions on convergence rate results in the existing literature are presented. Numerical results validate the findings. [ABSTRACT FROM AUTHOR]

Fault tolerance for asynchronous sequential machines (ASMs) is studied in the framework of corrective control theory. The considered ASM is subjected to adversarial inputs entering the closed-loop system through control input and state feedback channels. If the adversarial input occurs at the control input channel, the machine undergoes unauthorized state transitions. If the adversarial input occurs at the feedback channel, it distorts the state feedback value that is transmitted to the controller. We present a scheme of fault diagnosis on each fault event and the existence condition and design procedure for a corrective controller that invalidates any fault occurrence in an asynchronous mechanism. An illustrative example is provided to validate the proposed fault diagnosis and fault tolerant control methodology. [ABSTRACT FROM AUTHOR]

We present a reset control approach to improve the transient performance of a PID-controlled motion system subject to Coulomb and viscous friction. A reset integrator is applied to circumvent the depletion and refilling process of a linear integrator when the solution overshoots the setpoint, thereby significantly reducing the settling time. Robustness for unknown static friction levels is obtained. The closed-loop system is formulated through a hybrid systems framework, within which stability is proven using a discontinuous Lyapunov-like function and a meagre-limsup invariance argument. The working principle of the proposed reset controller is analyzed in an experimental benchmark study of an industrial high-precision positioning machine. [ABSTRACT FROM AUTHOR]

This paper presents a distributed event-based high gain feedback design for the cooperative global practical output regulation problem of nonlinear multi-agent systems with unit relative degree subject to the general nonlinear leader system. We first convert global practical output regulation problem into global practical stabilization problem, then prove the input-to-state stability of the closed-loop system by regarding the sampling error and the steady-state of the actuator together as the external input. Based on the high gain feedback technique, the input-to-state gain function can be made sufficiently small, and hence the tracking error can converge to an arbitrary predefined small residual set around the origin. A distinguishing feature of our result is that, our controller is static and purely digital, thus, giving rise to quite a simple structure. [ABSTRACT FROM AUTHOR]

In this paper, a new finite-horizon H ∞ control problem is considered for a class of time-varying systems with stochastic nonlinearities, measurements degradation and chance constraints. The purpose of the addressed problem is to design the time-varying controller such that the closed-loop system satisfies the prespecified H ∞ disturbance attenuation requirement and certain chance constraints on the controlled output vector z k (i.e., the probability of the controlled output z k belonging to a given set is larger than a prescribed value). A modified maximum-volume-inscribed-ellipsoid (MVIE) method is employed to convert the chance constraint into some tractable inequalities, which could be conveniently handled by the recursive linear matrix inequality (RLMI) approach. Then, by using stochastic control analysis method, sufficient conditions are derived for the existence of the desired multi-objective controller and, furthermore, the gains of the desired controllers are characterized by means of RLMIs. Finally, two illustrative examples and a practical system are proposed to highlight the effectiveness and applicability of the presented controller design technology. [ABSTRACT FROM AUTHOR]

This paper deals with the stability of linear stochastic systems in the presence of sporadic measurements and communication delays. Motivated by considerations about the efficient use of the available resources, two so-called dynamic discrete-time event-triggered control (DTETC) strategies tailored to the system are designed, including some existing periodic event-triggered control strategies as particular cases. An impulsive switched system approach and a switched time-delay system approach are developed for modeling and stability analysis of the resulting closed-loop systems, respectively. In addition, it is shown that under the same decay rate, the designed dynamic DTETC may further reduce the conservatism than their static counterparts. Interestingly, the proposed impulsive switched system approach can capture the stabilizing effect of the communication delays. A numerical example is provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]