Solving linear optimal control problems of the timedelayed systems by Adomian decomposition method

We apply the Adomian decomposition method (ADM) to obtain a subop timal control for linear timevarying systems with multiple state and control delays and with quadratic cost functional. In fact, the nonlinear twopoint 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 timevarying multidelay systems. Some illustrative examples are employed to demonstrate the accuracy and efficiency of the proposed methods.