Patchy Solution of a Francis-Byrnes-Isidori Partial Differential Equation
arXiv:1106.5815 · doi:10.1002/rnc.2776
Abstract
The solution to the nonlinear output regulation problem requires one to solve a first order PDE, known as the Francis-Byrnes-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. With our method we are able to produce approximations that converge uniformly to the true solution. Our method relies on the periodic nature of two-dimensional analytic center manifolds.
21 pages, 12 figures