Dynamic Output Feedback Control Law Research Articles

Adaptive distributed observer design for containment control of heterogeneous discrete-time swarm systems

This paper develops both adaptive distributed dynamic state feedback control law and adaptive distributed measurement output feedback control law for heterogeneous discrete-time swarm systems with multiple leaders. The convex hull formed by the leaders and the system matrix of leaders is estimated via an adaptive distributed containment observer. Such estimations will feed the followers so that every follower can update the system matrix of the corresponding adaptive distributed containment observer and the system state of their neighbors. The followers cooperate with each other to achieve leader–follower consensus and thus solve the containment control problem over the network. Numerical results demonstrate the effectiveness and computational feasibility of the proposed control laws.

Cooperative Output Regulation of Linear Multiagent Systems: An Event-Triggered Adaptive Distributed Observer Approach

This article investigates the cooperative output regulation problem for heterogeneous linear multiagent systems by event-triggered control, where the system matrix of the exosystem is not available to all agents. First, an event-triggered adaptive distributed observer is designed for each agent to estimate both the state and the system matrix of the exosystem. Then, a fully distributed event-triggered dynamic output feedback control law is proposed for each agent. Meanwhile, a fully distributed event-triggering mechanism is proposed such that each agent can determine when to broadcast its information to its neighbors. It is shown that with the proposed event-triggered control strategy, the cooperative output regulation problem is solved by intermittent communication in a fully distributed manner in the sense that no global information, such as the eigenvalues of the Laplacian matrix or the number of the agents, is used. It is also shown that Zeno behavior is excluded for each agent. Finally, a numerical example is given to illustrate the effectiveness of the proposed event-triggered control strategy.

Dynamic output nonfragile reliable control for nonlinear fractional-order glucose–insulin system

The main intention of this paper is to scrutinize the problem of internal model-based dynamic output feedback nonfragile reliable control problem for fractional-order glucose–insulin system. Specifically, a robust control law that represents the insulin injection rate is designed in order to regulate the level of glucose in diabetes treatment in the existence of meal disturbance or external glucose infusion due to improper diet. By the construction of suitable Lyapunov functional, a novel set of sufficient conditions is derived with the aid of linear matrix inequalities for obtaining the required dynamic output feedback control law. In particular, the designed controller ensures the robust stability and disturbance attenuation performance against meal disturbance of the glucose–insulin system. Numerical simulation results are performed to verify the advantage of the developed design technique. Specifically, the irregular blood glucose level can be brought down to normal level by injecting suitable rate of insulin to the patient. The result exposes that the level of blood glucose is sustained in the identified ranges via the proposed dynamic output feedback control law.

The Adaptive Distributed Event-Triggered Observer Approach to Cooperative Output Regulation of Discrete-Time Linear Multi-Agent Systems Under Directed Switching Networks

In the paper, we solve the cooperative output regulation problem of discrete-time linear multi-agent systems under directed switching networks. Firstly, a new adaptive distributed event-triggered observer is proposed, which does not require each follower to know the leader matrix information. In addition, we propose relative threshold and novel switching threshold event-triggered strategy, which can be used in different situations according to their respective characteristics. Then, we solve the cooperative output regulation problem for discrete-time linear multi-agent systems under directed switching networks by both distributed state feedback and distributed dynamic output feedback control laws utilizing the adaptive distributed event-triggered observer. Finally, a corresponding numerical simulation on the discrete-time linear multi-agent systems is conducted, and the cooperative output regulation performance is verified.

Output regulation of linear systems via sampled-data control

In this paper, we study the output regulation problem for linear systems by the aperiodic sampled-data control approach. Suppose the problem is solvable by a continuous-time static state feedback control law and a continuous-time dynamic output feedback control law. Then, we first show that, if the exogenous signal is constant, then the output regulation problem is solvable exactly by both the sampled-data static state feedback control law and the sampled-data dynamic output feedback control law. If the exogenous signal is time-varying with bounded derivative, then we further show that the problem is solvable practically by both the sampled-data static state feedback control law and the sampled-data dynamic output feedback control law.

Output feedback robust MPC for linear systems with norm-bounded model uncertainty and disturbance

This paper presents an output feedback robust model predictive control strategy for linear systems with norm-bounded model parametric uncertainty and disturbance. In order to reduce the computational burden and enhance the control performance, in the optimization problem we optimize the estimator state matrix instead of the state estimator gain. The infinite horizon control moves and estimated states are parameterized by a dynamic output feedback control law, where its state feedback gain and estimator state matrix are optimized at each sampling instant. By appropriately refreshing the estimation error set, the optimization problem is shown to be recursively feasible and the convergence of the augmented state is guaranteed. A numerical example is given to show the effectiveness of the proposed approach.

Robust output regulation of discrete-time linear systems by quantized output feedback control

This technical communique studies the robust output regulation problem of uncertain discrete-time linear systems by quantized output feedback control. We show that, under the same assumptions as those that guarantee the solvability of the robust output regulation problem by a dynamic output feedback control law, our problem is also solvable by a dynamic quantized output feedback control law as long as the quantization density is greater than certain explicitly specified lower bound.

Distributed Dynamic Event-Triggered Control for Cooperative Output Regulation of Linear Multiagent Systems.

This paper investigates the cooperative output regulation problem for heterogeneous linear multiagent systems under fixed communication graphs via event-triggered control. A fully distributed event-triggered dynamic output feedback control law is proposed based on the feedforward design approach. At the same time, a fully distributed dynamic event-triggering mechanism is designed so that each agent can determine when to broadcast its information to its neighbors. Compared with existing related results, both the control law and the event-triggering mechanism in this paper are independent of any global information. It is shown that with the proposed dynamic event-triggered control strategy, the cooperative output regulation problem can be solved in a fully distributed manner by intermittent communication. Moreover, Zeno behavior can be strictly ruled out for each agent. Finally, the effectiveness of the proposed dynamic event-triggered control strategy is validated by a numerical example.

Target tracking for non-identical high-order networks based on reduced-order observers

ABSTRACTIn this paper, target tracking for non-identical high-order networks is presented under the digraph network topology. The target agent has different dimensions with the followers. We first address a distributed dynamic state feedback control law to solve the output tracking problem. Then a reduced-order observer is designed, and an observer-based dynamic output feedback control law is given for the case that the states of the agents are not fully measurable. Finally, some simulation results are given to illustrate the validity of the theoretical results.

Resilient First-Order Consensus and Weakly Stable, Higher Order Synchronization of Continuous-Time Networked Multiagent Systems

Local interaction rules for consensus and synchronization are vital for many applications in distributed control of cyber-physical systems. However, most research in this area assumes all nodes (or agents) in the networked system cooperate. This paper considers local interaction rules for resilient first-order consensus and weakly stable, higher order synchronization whenever some of the agents in the network are Byzantine-like adversaries defined in a continuous-time setting. The normal agents have identical dynamics modeled by continuous-time, linear, time-invariant, weakly stable systems. Agents in the networked system influence one another by sharing state or output information according to a directed, time-varying graph. We present a resilient consensus protocol as well as dynamic state and output feedback control laws for the normal agents, to achieve the resilient consensus and synchronization objectives, respectively. We characterize the required network topologies using the property of network robustness. We demonstrate the results in simulation examples to illustrate the resilient synchronization output feedback control law.

Distributed-observer-based output synchronization for heterogeneous double-integral networks

This paper considers the output synchronization for nonidentical second-order integral dynamics with external disturbance. The leader’s signal can only be received by parts of the followers, and all the followers have different dynamics. An adaptive distributed compensator is utilized to estimate the leader’s signal and system matrix. Since the states’ information of the agents can not be measured by the others, a novel distributed reduced-dimension observer is designed to estimate the unmeasurable states. Based on the adaptive distributed compensator and reduced-dimension observer, a dynamic output feedback control law is designed to solve the output synchronization problem. Finally, an example is given to illustrate the validity of the theoretical results.

Robust output consensus of networked heterogeneous nonlinear systems by distributed output regulation

In this paper, we study the output consensus problem of networked heterogeneous nonlinear systems. In contrast to existing results on similar problems, output consensus of all systems is achieved with some robustness not only to heterogeneous dynamics with uncertainties but also to unreliable network communication in terms of network connectivity and communication delays. In particular, we allow the time-varying network topology and the presence of time-varying communication delays in network, which are among the most challenging issues in cooperative control. To solve the problem, we propose a hierarchical control scheme and design a distributed dynamic output feedback control law by the distributed output regulation approach. The proposed control approach offers great flexibility to incorporate the output regulation approach, the separation principle and the certainty equivalence principle to stability analysis of the closed-loop system, thus setting a stage for systematically studying the robust output consensus problem. By establishing some technical lemmas and resorting to ISS Lyapunov technique, we solve the robust output consensus problem of nonlinear multi-agent systems subject to system uncertainties, jointly connected directed network topologies, and arbitrarily bounded and nonuniform time-varying communication delays.

Active vibration robust control for FGM beams with piezoelectric layers

The dynamic output-feedback robust control method based on linear matrix inequality (LMI) method is presented for suppressing vibration response of a functionally graded material (FGM) beam with piezoelectric actuator/sensor layers in this paper. Based on the reduced model obtained by using direct mode truncation, the linear fractional state space representation of a piezoelectric FGM beam with material properties varying through the thickness is developed by considering both the inherent uncertainties in constitution material properties as well as material distribution and the model error due to mode truncation. The dynamic output-feedback robust H-infinity control law is implemented to suppress the vibration response of the piezoelectric FGM beam and the LMI method is utilized to convert control problem into convex optimization problem for efficient computation. In numerical studies, the flexural vibration control of a cantilever piezoelectric FGM beam is considered to investigate the accuracy and efficiency of the proposed control method. Compared with the efficient linear quadratic regulator (LQR) widely employed in literatures, the proposed robust control method requires less control voltage applied to the piezoelectric actuator in the case of same control performance for the controlled closed-loop system.

Robust output synchronization of heterogeneous nonlinear agents in uncertain networks

This paper investigates the global robust output synchronization problem for a class of nonlinear multi-agent systems. In the considered setup, the controlled agents are heterogeneous and with both dynamic and parametric uncertainties, the controllers are incapable of exchanging their internal states with the neighbors, and the communication network among agents is defined by an uncertain simple digraph. The problem is pursued via nonlinear output regulation theory and internal model based design. For each agent, the input-driven filter and the internal model compose the controller, and the decentralized dynamic output feedback control law is derived by using backstepping method and the modified dynamic high-gain technique. The theoretical result is applied to output synchronization problem for uncertain network of Lorenz-type agents.

Cooperative output regulation of discrete-time linear time-delay multi-agent systems under switching network

In this paper, we study the cooperative output regulation problem for discrete-time linear time-delay multi-agent systems subject to jointly connected switching networks. Our distributed control law is composed of a purely decentralized control law and a distributed switched observer. In contrast to the same problem with static networks, the closed-loop system of this paper is a switched system, the stability analysis of the closed-loop system cannot be conducted by the existing frequency domain technique. Therefore, we need to establish two lemmas to lay the foundation for solving the problem and then present the solution to the problem by a distributed dynamic output feedback control law. An example is used to illustrate our approach.

Consensus of linear multi‐agent systems subject to communication delays and switching networks

SummaryIn this paper, the consensus problem for linear multi‐agent systems subject to nonuniform time‐varying communication delays and jointly connected switching networks is investigated. Two cases, known communication delay and unknown communication delay, are considered, respectively. For each case, both distributed dynamic state feedback control law and distributed dynamic output feedback control law are proposed. By establishing some technical lemmas, it is shown that the proposed distributed control laws can solve the consensus problem, respectively. Copyright © 2017 John Wiley & Sons, Ltd.

Regional Stability Analysis of Discrete-Time Dynamic Output Feedback Under Aperiodic Sampling and Input Saturation

This technical note addresses the problem of regional stability analysis of a continuous-time plant controlled by a discrete-time dynamic output feedback control law with saturation constraints under aperiodic sampling. To cope with the aperiodic sampling problem, the proposed approach is based on an impulsive system modeling and the use of looped functionals. A generalized sector-based relation is applied to tackle the control saturation effects. From these ingredients, conditions to ensure regional asymptotic stability of the closed-loop system under aperiodic sampling are derived. Based on these conditions, LMI-based optimization problems are proposed to compute estimates of the region of attraction of the closed-loop system or to maximize the bound on the maximal admissible interval between two successive sampling instants, for which the regional stability can be ensured with respect to a given set of admissible states. A numerical example illustrates the application of the results.

Cooperative output regulation of discrete‐time linear time‐delay multi‐agent systems

In this paper, we study the cooperative output regulation problem for the discrete linear time-delay multi-agent systems by distributed observer approach. In contrast with the same problem for continuous-time linear time-delay multi-agent systems, the problem has two new features. First, in the presence of time-delay, the regulator equations for discrete-time linear systems are different from those for continuous-time linear systems. Second, under the standard assumption on the connectivity of the communication graph, a distributed observer for any continuous-time linear leader system always exists. However, this is not the case for the discrete counterpart of the distributed observer for the continuous-time systems. Another type of discrete distributed observer is proposed. It turns out that such an observer always exists under some mild assumptions. Using this result, the authors further present the solvability conditions of the problem by distributed dynamic output feedback control law.

Event-Triggered Output Feedback Stabilization via Dynamic High-Gain Scaling

This paper addresses output feedback stabilization via event-triggered output feedback. In the first part of the paper, linear systems are considered, whereas the second part shows that a dynamic event-triggered output feedback control law can achieve feedback stabilization of the origin for a class of nonlinear systems by employing dynamic high-gain techniques.

Bipartite consensus of multi-agent systems over signed graphs: State feedback and output feedback control approaches

Summary This paper studies bipartite consensus problems for continuous-time multi-agent system over signed directed graphs. We consider general linear agents and design both state feedback and dynamic output feedback control laws for the agents to achieve bipartite consensus. Via establishing an equivalence between bipartite consensus problems and the conventional consensus problems under both state feedback and output feedback control approaches, we make direct application of existing state feedback and output feedback consensus algorithms to solve bipartite consensus problems. Moreover, we propose a systematical approach to design bipartite consensus control laws. Copyright © 2016 John Wiley & Sons, Ltd.