Example of output regulation for a system with unbounded inputs andoutputs

摘要

We give an explicit example of an extension by Byrnes et al.(1999) of the geometric approach to the design of feedback laws forsolving the regulator problem for regular linear control systems. Theapproach used in the above mentioned article is based on another paper(Byrnes et al., 1998) which treats the infinite dimensional theory ofoutput regulation for bounded control and observation operators. In thefirst mentioned article, the authors have characterized the solvabilityof both state and error feedback regulator problems in terms of thesolvability of certain regulator equations in the case of unboundedinput and output operators. In this paper we present a simple example ofset point control for a one dimensional heat equation. We have selecteda simple example for which analytic and numerical solutions are readilyobtained and the explicit implementation of these feedback designstrategies can be easily identified