Example of output regulation for a system with unbounded inputs and outputs

We give an explicit example of an extension by Byrnes et al. (1999) of the geometric approach to the design of feedback laws for solving the regulator problem for regular linear control systems. The approach used in the above mentioned article is based on another paper (Byrnes et al., 1998) which treats the infinite dimensional theory of output regulation for bounded control and observation operators. In the first mentioned article, the authors have characterized the solvability of both state and error feedback regulator problems in terms of the solvability of certain regulator equations in the case of unbounded input and output operators. In this paper we present a simple example of set point control for a one dimensional heat equation. We have selected a simple example for which analytic and numerical solutions are readily obtained and the explicit implementation of these feedback design strategies can be easily identified