Approximation design of composite control for singularly perturbed time-delay systems via delay compensation

The approximation design problem of linear quadratic composite control for singularly perturbed time-delay system is considered. Based on the slow-fast decomposition theory of singular perturbation, the original optimal control problem is decomposed into a fast subproblem without time-delay and a slow time-delay subproblem. To obtain the numerical solution of optimal control law of the slow subproblem, the two-point boundary value problem is first transformed into a new one formulated by state and delay compensation vectors, and then the shooting method is used to solve the problem. Further, the composite control law of the original problem is obtained. Numerical example is presented to illustrate the effectiveness of the proposed method.