Policy iteration optimal tracking control for chaotic systems by using an adaptive dynamic programming approach**Project supported by the National Natural Science Foundation of China (Grant Nos. 61034002, 61233001, 61273140, 61304086, and 61374105) and the Beijing Natural Science Foundation, China (Grant No. 4132078).

Abstract

A policy iteration algorithm of adaptive dynamic programming (ADP) is developed to solve the optimal tracking control for a class of discrete-time chaotic systems. By system transformations, the optimal tracking problem is transformed into an optimal regulation one. The policy iteration algorithm for discrete-time chaotic systems is first described. Then, the convergence and admissibility properties of the developed policy iteration algorithm are presented, which show that the transformed chaotic system can be stabilized under an arbitrary iterative control law and the iterative performance index function simultaneously converges to the optimum. By implementing the policy iteration algorithm via neural networks, the developed optimal tracking control scheme for chaotic systems is verified by a simulation.