Robust output regulation of a thermoelastic system

In this paper, we consider the robust output regulation problem for the thermoelastic system where the boundary control input and the output are located at the left end of the wave equation and the disturbance input is located at the right end of the heat equation. We formulate the system as a boundary control system and prove that it is impedance passive and well-posed. We design a finite-dimensional controller based on the internal model principle and show that the controller can achieve robust output tracking and disturbance rejection. The numerical simulations demonstrate that the finite-dimensional dynamic error feedback controller can make the output track the reference signal asymptotically and the state of the closed-loop system is bounded.