Disturbance rejection control for discrete time-delay nonlinear system

This paper studies disturbance rejection problem for discrete time-delay nonlinear systems. The optimal control of original systems causes a nonlinear Two Points Boundary Value (TPBV) problem with both time-delay terms and time-advanced terms. By using of Successive Approximation Approach (SAA), the original nonlinear TPBV problem is transformed into a sequence of nonhomogeneous linear TPBV problems without time-delay terms and time-advanced terms. We proved that the sequence of solutions uniformly converges to the optimal disturbance rejection control law of the original systems through two lemmas. By finite iterations of the solution sequence, the iterative procedure can be stopped and suboptimal control law is obtained. Based on reduced-order disturbance observer, the presented control law can be easily completed and physically realizable. Simulation results of two cases verify the validity and effectiveness of the presented controller.