Patchy Solution of a Francis-Byrnes-Isidori Partial Differential Equation

Details Patchy Solution of a Francis-Byrnes-Isidori Partial Differential Equation Patchy Solution of a Francis-Byrnes-Isidori Partial Differential Equation

2011-06-28

arxiv.org/abs/1106.5815v1

Mathematics

Optimization and Control

21 pages, 12 figures

Scientific paper

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.

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