Robust output regulation for linear systems with structured uncertainty

This paper deals with the problem of robust tracking and disturbance rejection for a linear time-invariant system where the uncertainty of the system is represented in a structured form and the output to be controlled may be different from the measurement output. First, the problem is considered in a rather classical setting in that the required property of tracking and disturbance rejection can be attained as long as the resulting closed-loop system remains stable. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers having the robust tracking and disturbance rejection property. Second, the problem of robust output regulation with robust stability is formulated as one of finding a controller such that the resulting closed-loop system satisfies an additional requirement of robust stability and thus the output regulation property can be maintained for all perturbations of uncertain parameters within a prescribed set. A procedure based on a high gain observer approach is proposed to solve this problem.

Introduction: the basic ingredients of asymptotic output regulation the computation of the steady-state response highlights of output regulation for linear systems. Output regulation of nonlinear systems: the regulator equations the internal model necessary and sufficient conditions for local output regulation the special case of harmonic exogenus inputs approximate regulation. Existence conditions for regulator equations: linear regulator equations and transmission zeros the zero dynamics of a nonlinear system existence of solutions of the nonlinear regulator equations. Robust output regulation: structurally stable local regulation robust local regulation the special case of systems in triangular form a globally defined error-zeroing invariant manifold semiglobal robust regulation.

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

This article investigates the robust optimal output regulation problem for the constrained uncertain nonlinear systems. A two‐step design framework is proposed to overcome the difficulties brought by uncertainties, constraint and performance optimization. First, the feedforward controller is designed by the internal model principle, and the robust output regulation problem is transformed into the robust stabilization problem. Then, the optimal control problem with input saturation is further considered in the robust feedback controller design process. With the help of a non‐quadratic cost functional, actor‐critic algorithm and robust redesign technique are brought together to design the constrained robust optimal feedback controller. Finally, stability analysis based on Lyapunov method shows that all the signals of the closed‐loop system remain bounded, and the tracking error is uniformly ultimately bounded with arbitrarily small ultimate bound. Simulation results illustrate the effectiveness of the proposed methodology.

Output regulation aims to achieve, in addition to closed-loop stability, asymptotic tracking and disturbance rejection for a class of reference inputs and disturbances. Thus, it poses a more challenging problem than stabilization. For over a decade, the nonlinear output regulation problem has been one of the focuses in nonlinear control research, and active research on this problem has generated many fruitful results. Nevertheless, there are two hurdles that impede the further progress of the research on the output regulation problem. The first one is the assumption that the solution or the partial solution of the regulator equations is polynomial. The second one is the lack of a systematic mechanism to handle the global robust output regulation problem. We establish a general framework that systematically converts the robust output regulation problem for a general nonlinear system into a robust stabilization problem for an appropriately augmented system. This general framework, on one hand, relaxes the polynomial assumption, and on the other hand, offers a greater flexibility to incorporate recent new stabilization techniques, thus setting a stage for systematically tackling the robust output regulation with global stability.

The topic of this paper is the backstepping-based solution of the robust state feedback regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients. Thereby, a large class of outputs is considered, i.e., mixed distributed and pointwise in-domain or boundary outputs. The state feedback regulator design is based on the $\boldsymbol {p}$ -copy internal model principle. This results in a stabilization problem for a cascade of $\boldsymbol {m+p}$ boundary controlled transport partial differential equations (PDEs) with $\boldsymbol {p}$ ordinary differential equations (ODEs). For this, a systematic backstepping approach is presented, in which all design equations are explicitly solvable in backstepping coordinates. Furthermore, the solvability conditions for the considered output regulation problem can be evaluated in closed form utilizing the plant transfer behavior. Robust output regulation is verified for nondestabilizing model uncertainties and unknown disturbance input locations. A $\boldsymbol {4 \times 4}$ hyperbolic system with uncertain transport velocities and couplings in the transport PDEs illustrates the results of this paper.

The cooperative output regulation of a linear multi-agent system can be viewed as a generalization of the leader-following consensus problem and was studied recently for the case where the system uncertain parameters vary in a sufficiently small neighborhood of their nominal value. This case was handled by the internal model design which converts the problem into a simultaneous eigenvalue placement problem of an augmented multi-agent system. In this paper, we further consider the cooperative robust output regulation problem for a class of minimum phase linear multi-agent systems in the sense that the controller allows the system uncertain parameters to vary in an arbitrarily prescribed compact subset. For this purpose, we introduce a new type of internal model that allows the cooperative robust output regulation problem of the given plant to be converted into a robust stabilization problem of an augmented multi-agent system. We then solve our problem by combining a simultaneous high-gain state feedback control technique and a distributed high-gain observer technique. A special case of our result leads to the solution of the leader-following robust consensus problem for a class of uncertain multi-agent systems. Copyright © 2013 John Wiley & Sons, Ltd.

Chapter 2 considers exact output regulation for linear systems. As defined there, solving an output regulation problem involves constructing an appropriate state or measurement feedback controller that renders the closed-loop system internally stable (as usual, for internal stability we disregard the exosystem) while the tracking error tends to zero as the time t tends to infinity. In this chapter, we revisit the output regulation problem however for linear continuous-time systems with actuators subject to amplitude saturation.KeywordsState FeedbackFeedback ControllerSolvability ConditionOutput RegulationRegulator EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A global state feedback output regulating control for uncertain systems in strict feedback form

In this paper, robust output regulation problems of singular linear systems are studied. Under appropriate assumptions, it is given that the solvability of robust output regulation problems equals to a specifically row full rank matrix. Moreover, the methods for constructing the feedback regulator are discussed.

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

Cooperative robust output regulation for heterogeneous second-order discrete-time multi-agent systems

This paper studies a robust output regulation problem with nonlinear exosystems without the assumption that the solution to the regulator equations along the trajectory of the exosystems should be polynomial. Based on the extended concepts of steady-state generator and internal model, a set of sufficient conditions for the solvability of the problem are given. Thus, the result developed in this paper can allow the robust output regulation problem with nonlinear exosystems to accommodate much more general nonlinear given plants including those which contain nonpolynomial nonlinearity.

In this paper, we study the cooperative global robust practical output regulation problem for a class of second-order uncertain nonlinear multiagent systems via a distributed event-triggered state feedback control strategy. Compared with the existing work, one of the main challenges is that we need to design two distributed internal models to learn both the desired steady-state state and steady-state input for each agent. Moreover, to obtain a directly implementable digital control law, the two distributed internal models of each agent only depend on the sampled states of the neighboring agents and itself. As a result, the resulting augmented system is more complicated, and the control law needs to be recursively designed. To overcome the difficulty, we propose a novel distributed event-triggered control law and a novel distributed event-triggered mechanism to deal with our problem. By adjusting a design parameter in the proposed event-triggered mechanism, we show that the Zeno behavior does not happen and the ultimate bound of the tracking error can be made arbitrarily small. Our design will be illustrated by two examples.

This paper addresses the robust output regulation of linear heterogeneous multi-agent systems under switching and undirected network topology. Due to uncertain parameters in every agent or subsystem, an internal model method is adopted in the sense that the controller allows the system uncertain parameters to vary in a neighborhood of the nominal system. By designing two kinds of appropriate distributed control scheme, output regulation problem is well solved. A numerical example is presented to illustrate the effectiveness of the proposed method.