Approximate Optimal Tracking Control for a Class of Nonlinear Systems with Disturbances

This paper develops an approximate design procedure of optimal tracking controllers for a class of nonlinear systems with persistent disturbances in the infinite time domain. By using the successive approximation approach (SAA), the two-point boundary value (TPBV) problem, which is derived from the optimal control theory, is transformed into solving a sequence of linear TPBV problems. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original optimal tracking control (OTC) problem. A feedforward and feedback optimal tracking control (FFOTC) law is derived from a Riccati equation, matrix equations and a sequence of adjoint vectors. The existence and uniqueness conditions of the FFOTC are given. At last, a design algorithm of solving the approximate FFOTC law is proposed, and simulation results demonstrate the validity of the algorithm