Solving linear optimal control problems of the time-delayed systems by Adomian decomposition method

We apply the Adomian decomposition method (ADM) to obtain a subop timal control for linear time-varying systems with multiple state and control delays and with quadratic cost functional. In fact, the nonlinear two-point boundary value problem, derived from Pontryagin’s maximum principle, is solved by ADM. For the first time, we present here a convergence proof for ADM. In order to use the proposed method, a control design algorithm with low computational complexity is presented. Through the finite iterations of algorithm, a suboptimal control law is obtained for the linear time-varying multi-delay systems. Some illustrative examples are employed to demonstrate the accuracy and efficiency of the proposed methods.