Output regulation for a boundary controlled two-dimensional heat equation

Output regulation includes the sat of problems concerned with controlling a system so that its output will track the output generated by an external system, or exogenous system. These problems are commonly studied in Classical Control Theory and have several forms, soma of which are widely studied and understood, while others are lass so.

Problems of output regulation for systems governed by Ordinary Differential Equations (ODE's) have been heavily studied, while for systems governed by Partial Differential Equations (PDE's) the corresponding problems have been study to a lesser degree. For either case, the exosystem, which generates the signals to be tracked, has always been taken to be finite dimensional. In this work, we are concerned with output regulation problems for a boundary controlled heat equation on a finite rectangle (infinite dimensional) when the exosystem is infinite dimensional being given by a one dimensional wave equation.