Patchy Solution of a Francis-Byrnes-Isidori Partial Differential Equation
This work addresses the computational challenge of solving the FBI equations for a specific class of systems, offering a theoretically guaranteed approximation method.
The paper proposes a method to compute approximate solutions to the Francis-Byrnes-Isidori PDE for nonlinear output regulation, achieving uniform convergence to the true solution for plants with hyperbolic zero dynamics and a two-dimensional exosystem.
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.