Nonlinear Optimal Controller Designs Satisfying State and Input Norm Constraints

Abstract

This paper deals with the optimal control problems of the nonlinear system with state or input norm constraints. To address the constrants, nonlinear weighting functions are introduced to a cost function. An optimal control law is solved via the stable manifold approach which is recently proposed for solving the Hamilton-Jacobi equation. The behavior of the proposed controller coincides with that of linear optimal controller within the constraints. The effectiveness of the proposed method is verified by a numerical example and a DC motor experiment.