Robust controllers for a heat equation using the Galerkin approximation

Abstract

We consider the robust output tracking problem for an unstable one-dimensional heat equation. As the main contribution we propose a new way of designing infinite-dimensional robust controllers based on Galerkin approximations of infinite-dimensional observer-based controllers. The results are illustrated with a concrete example where the finite-dimensional controllers are constructed using the Finite Element Method. The results are extendable for more general parabolic control systems.