Analytical approximation method for the center manifold in the nonlinear output regulation problem

In nonlinear output regulation problems, it is necessary to solve the so-called regulator equations consisting of a partial differential equation and an algebraic equation. It is known that, for the hyperbolic zero dynamics case, solving the regulator equations is equivalent to calculating a center manifold for zero dynamics of the system. The present paper proposes a successive approximation method for obtaining center manifolds and shows its effectiveness by applying it for an inverted pendulum example.