Iterative methods to compute center and center-stable manifolds with application to the optimal output regulation problem

This paper presents iterative methods for computing center and center-stable manifolds. The methods are based on the contraction mapping theorem and compute flows on the invariant manifolds. An important application includes the design of optimal output regulators. It will be shown that the center manifold algorithm solves the regulator equation and the center-stable manifold algorithm computes controllers for optimal output regulation.