Finite-Dimensional Controllers for Robust Regulation of Boundary Control Systems

We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the abstract setting and present finite-dimensional reduced order controllers. The controller design is then used for particular PDE models: high-dimensional parabolic equations and beam equations with Kelvin-Voigt damping. Numerical examples will be presented using Finite Element Method.