Optimal rejection with zero steady-state error to disturbances for a class of nonlinear systems with time-delay

The optimal disturbance rejection problem with zero steady-state error for a class of nonlinear systems with time-delay is considered. Based on the internal model principle, a disturbance compensator is designed to remove the influence of external disturbance. By using the maximum principle, the optimal control problem is constructed to solve the nonlinear two-point boundary value problem with both time-delay and time-advanced terms. The successive approximation approach is used to obtain the decoupling form of the optimal compensator and the optimal feedback term. Simulation results demonstrate the effectiveness of the optimal disturbance rejection control law.