Controller Design for Robust Output Regulation of Regular Linear Systems

We present three dynamic error feedback controllers for robust output regulation of regular linear systems. These controllers are i) a minimal order robust controller for exponentially stable systems, ii) an observer-based robust controller, and iii) a new internal model based robust controller structure. In addition, we present two controllers that are by construction robust with respect to predefined classes of perturbations. The results are illustrated with an example where we study robust output tracking of a sinusoidal reference signal for a 2-D heat equation with boundary control and observation.

I. Introduction

The topic of this paper is the construction of controllers for robust output regulation of linear infinite-dimensional systems. The goal in this control problem is to design a control law for a linear system

$$\begin{align*}\dot{x}(t)=&\,Ax(t)+Bu(t)+w(t),\quad x(0)=x_{0}\in X&\tag{1a}\\ y(t)=&\,Cx(t)+Du(t)&\tag{1b}\end{align*}$$ in such a way that the output converges asymptotically to a given reference signal despite the external disturbance signal . In addition, the controller must tolerate small perturbations and uncertainties in the parameters of the plant (1). The robust output regulation problem was first studied for finite-dimensional systems in the 1970's most notably by Francis and Wonham [6], [7], and Davison [4], and since then the theory of output regulation has been been actively developed for infinite-dimensional systems [2], [9], [11], [21], [22], [24].