An efficient recursive shooting method for the optimal control of time-varying systems with state time-delay

This paper presents a recursive shooting method for solving the optimal control problem of linear time-varying systems with state time-delay. In this approach, the original time-delay optimal control problem is first transformed into a sequence of linear two-point boundary value problems (TPBVPs) without delay and advance terms. Then, by using a shooting method for the solution of latter sequence in a recursive manner, an optimal control law is achieved which consists feedback and forward terms. The feedback term is determined by solving a matrix Riccati differential equation. The forward term is an infinite sum of adjoint vectors, which can be obtained by solving the above-mentioned sequence of linear non-delay TPBVPs. The convergence analysis of the proposed approach is also provided. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach. (C) 2015 Elsevier Inc. All rights reserved.