Approximate robust output regulation of 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.

29 pages, 4 figures

References in corpus (5)

• The Internal Model Principle for Systems with Unbounded Control and Observation
• Controller Design for Robust Output Regulation of Regular Linear Systems
• Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems
• Robust Regulation of Infinite-Dimensional Port-Hamiltonian Systems
• Robust Output Regulation for Continuous-Time Periodic Systems