Robust output regulation for multi-dimensional heat equation under boundary control

Over the past few years, the internal model principle has been extended to some systems described by one-dimensional partial differential equations (PDEs) from the PDE perspective. However, robustness has remained limited to specific cases, primarily due to the challenges in formulating it within the PDE framework. In this paper, we explore output regulation for a multi-dimensional heat equation under boundary control, where the output space is infinite-dimensional. We not only derive an analytic tracking error feedback control but also demonstrate robustness. This is achieved by leveraging abstract results and PDE design techniques.