The optimal damping control for nonlinear time-delaysystems with persistent disturbances is considered. Based onsuccessive approximation approach (SAA), the optimal dampingcontrol (ODC) law is achieved by solving a decoupled sequence ofinhomogeneous linear two-point boundary value (TPBV)problems without time-delay and time-advance terms. The ODClaw of the original problem consists of accurate state feedbackterm, disturbance rejection term and a nonlinear time-delaycompensation term, which is the limit of the adjoint vectorsequence. By using the finite-time iteration of the compensationsequence, we can obtain an approximate optimal disturbancerejection control law. The proposed algorithms not only solveoptimal control problems in the nonlinear time-delay system butalso reduce the computation time and improve the precision.Numerical examples are included to illustrate the procedures.
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