Analyses for optimal control of discrete time-delay systems based on ADP algorithm with finite-horizon performance index

An optimal control scheme is obtained for a class of nonlinear discrete time-delay systems in this paper. Based on adaptive finite-horizon dynamic programming (ADP) algorithm, we focus on two different initial control conditions, and then the value iteration method is used to get the iterative performance index function and iterative control. Two neural networks, which are named as critic network and action network are used to approximate the performance index function and compute the optimal control policy. The iteration termination error and the performance index function are analyzed based on different initial states. In the simulation study, we analysis the control results of different initial states and different maximal iterative steps.