This paper studies an approximation approach to optimal control for singularly perturbed time-delay systems.
Based on the slow-fast decomposition theory of singular perturbation, the optimal control problem is firstly decomposed into a fast subproblem and a slow one with time-delay. By using Chebyshev polynomial series method, the optimal control law design of the slow one is transformed into a problem of solving linear equations. Then, a suboptimal control law of the slow subproblem is developed by solving the linear equations. Further, the suboptimal control law of the original problem is obtained and formulated as base vectors of the Chebyshev polynomial series. Numerical example is presented to show the effectiveness of the proposed method.