Approximate robust output regulation of boundary control systems

TL;DR

This paper develops a finite-dimensional approximate robust controller for boundary control systems, extending the internal model principle to infinite-dimensional systems like wave equations, and demonstrates its effectiveness through numerical simulations.

Contribution

It introduces a finite-dimensional controller structure for approximate robust output regulation of boundary control systems, overcoming the infinite-dimensional limitations of exact solutions.

Findings

Successfully designed an approximate robust controller for a wave equation

Demonstrated controller performance via numerical simulations

Extended the internal model principle to boundary control systems

Abstract

We extend the internal model principle for systems with boundary control and boundary observation, and construct a robust controller for this class of systems. However, as a consequence of the internal model principle, any robust controller for a plant with infinite-dimensional output space necessarily has infinite-dimensional state space. We proceed to formulate the approximate robust output regulation problem and present a finite-dimensional controller structure to solve it. Our main motivating example is a wave equation on a bounded multidimensional spatial domain with force control and velocity observation at the boundary. In order to illustrate the theoretical results, we construct an approximate robust controller for the wave equation on an annular domain and demonstrate its performance with numerical simulations.