A Successive Approximation Approach of Nonlinear Optimal Control with R-Rank Persistent Disturbances

Abstract

A new feedforward and feedback optimal control law for a class of nonlinear systems with persistent disturbances is presented in this paper. By using a successive approximation approach (SAA), the original nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of analytical linear feedforward and feedback terms and a nonlinear compensation term which is the limit of the solution sequence for the adjoint vector differential equations. By using the finite-step iteration of nonlinear compensation sequence, we can obtain a feedforward and feedback suboptimal control law. A disturbance observer is designed to get a physically realizable controller. Simulation examples show the effectiveness of the approach.