Off-policy integral reinforcement learning optimal tracking control for continuous-time chaotic systems**Project supported by the National Natural Science Foundation of China (Grant Nos. 61304079 and 61374105), the Beijing Natural Science Foundation, China (Grant Nos. 4132078 and 4143065), the China Postdoctoral Science Foundation (Grant No. 2013M530527), the Fundamental Research Funds for the Central Universities, China (Grant No. FRF-TP-14-119A2), and the Open Research

Abstract

This paper estimates an off-policy integral reinforcement learning (IRL) algorithm to obtain the optimal tracking control of unknown chaotic systems. Off-policy IRL can learn the solution of the HJB equation from the system data generated by an arbitrary control. Moreover, off-policy IRL can be regarded as a direct learning method, which avoids the identification of system dynamics. In this paper, the performance index function is first given based on the system tracking error and control error. For solving the Hamilton–Jacobi–Bellman (HJB) equation, an off-policy IRL algorithm is proposed. It is proven that the iterative control makes the tracking error system asymptotically stable, and the iterative performance index function is convergent. Simulation study demonstrates the effectiveness of the developed tracking control method.