Numerical schemes for optimal control of nonlinear time-delay systems with external disturbances

In this paper, The homotopy perturbation method is employed to solve nonlinear time-delay systems affected by external persistent disturbances with quadratic performance index. By using the finite-step iteration of a sequence, we can get an approximate optimal control law by solving a Riccati matrix equation and two Stein matrix equations using successive approximation method. A numerical example is employed to verify the effectiveness of the proposed approach