A New Approach for a Class of Continuous-Time Chaotic Systems Optimal Control by Online ADP Algorithm

Abstract

In this chapter, an online adaptive dynamic programming (ADP) based optimal control scheme is developed for continuous-time chaotic systems. The idea is to use ADP algorithm to obtain the optimal control input which makes the performance index function reach the optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to get the optimal control law. In the ADP structure, the neural networks are used to construct the critic network and action network, which can obtain the approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Simulation results are given to illustrate the performance of the established optimal control method.