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.
Tremendous amount of data are being generated and saved in many complex engineering and social systems every day.It is significant and feasible to utilize the big data to make better decisions by machine learning techniques. In this paper, we focus on batch reinforcement learning(RL) algorithms for discounted Markov decision processes(MDPs) with large discrete or continuous state spaces, aiming to learn the best possible policy given a fixed amount of training data. The batch RL algorithms with handcrafted feature representations work well for low-dimensional MDPs. However, for many real-world RL tasks which often involve high-dimensional state spaces, it is difficult and even infeasible to use feature engineering methods to design features for value function approximation. To cope with high-dimensional RL problems, the desire to obtain data-driven features has led to a lot of works in incorporating feature selection and feature learning into traditional batch RL algorithms. In this paper, we provide a comprehensive survey on automatic feature selection and unsupervised feature learning for high-dimensional batch RL. Moreover, we present recent theoretical developments on applying statistical learning to establish finite-sample error bounds for batch RL algorithms based on weighted Lpnorms. Finally, we derive some future directions in the research of RL algorithms, theories and applications.
