Piecewise smooth solutions to the nonlinear output regulation PDE

Abstract

The solution to the nonlinear output problem requires one to solve a first order PDE, known as the Francis-Byrne-Isidori (FBI) equations. In this paper we propose a method to compute approximate solutions to the FBI equations when the zero dynamics of the plant are hyperbolic and the exosystem is two-dimensional. Our method relies on the periodic nature of two-dimensional analytic center manifolds.