Robust Output Regulation for Multi-Dimensional Heat Equation

Abstract

In the past few years, we have developed internal model principle for some 1-d partial differential equations (PDEs) from PDE perspective, by which one can find the analytic form of the tracking error feedback control. However, the conditional robustness is only limited to some special cases because it is difficult to formulate the conditional robustness in the framework of PDEs. In this paper, we investigate output regulation for a boundary controlled multidimensional heat equation. We obtain not only an analytic tracking error feedback control but also prove the conditional robustness. This is a first time to combine the abstract result and PDE design, which takes advantages of both frameworks.