Approximate robust output regulation of boundary control systems

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