Optimal disturbance rejection control for a class of nonlinear system with control time-delay by model transformation method

The optimal control problem for nonlinear systems with control time-delay affected by external disturbance is considered. A model transformation is first presented, which transforms the nonlinear system with time-delay into a system without delay formally. To solve the optimal control problem for nonlinear systems with time-delay is transformed into optimal control problem for non-delay nonlinear systems. Based on the optimal control theory, the two-point boundary value (TPBV) problem is constructed. By using the successive approximation approach, the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear TPBV problems. we get approximate optimal control law by solving a Riccati matrix equation and two Stein matrix equations using successive approximation method. A simulation example shows that the approximate approach is effective and robust with respect to exogenous persistent disturbances.