Analytic Approximate Solution to The Nonlinear Output Regulation Problem Using Galerkin Approximation Method

The present paper proposes an approximation method to solve the problem of approximate nonlinear output regulation. In this approach, the solution of the regulator equations, consists of partial differential equations and an algebraic equation, is analytically approximated by Galerkin approximation method. The proposed method is general and can be applied on a wide class of nonlinear systems that the output regulation problem is solvable for them. The effectiveness of the proposed method is investigated on the nonlinear output regulation problem for a benchmark mechanical system, the so-called TORA system.