Chaotic system optimal tracking using data-based synchronous method with unknown dynamics and disturbances  

作　　者：宋睿卓 魏庆来 

机构地区：[1]School of Automation and Electrical Engineering, University of Science and Technology Beijing [2]The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation,Chinese Academy of Sciences

出　　处：《Chinese Physics B》2017年第3期268-275,共8页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.61304079,61673054,and 61374105);the Fundamental Research Funds for the Central Universities,China(Grant No.FRF-TP-15-056A3);the Open Research Project from SKLMCCS,China(Grant No.20150104)

摘　　要：We develop an optimal tracking control method for chaotic system with unknown dynamics and disturbances. The method allows the optimal cost function and the corresponding tracking control to update synchronously. According to the tracking error and the reference dynamics, the augmented system is constructed. Then the optimal tracking control problem is defined. The policy iteration （PI） is introduced to solve the rain-max optimization problem. The off-policy adaptive dynamic programming （ADP） algorithm is then proposed to find the solution of the tracking Hamilton-Jacobi- Isaacs （HJI） equation online only using measured data and without any knowledge about the system dynamics. Critic neural network （CNN）, action neural network （ANN）, and disturbance neural network （DNN） are used to approximate the cost function, control, and disturbance. The weights of these networks compose the augmented weight matrix, and the uniformly ultimately bounded （UUB） of which is proven. The convergence of the tracking error system is also proven. Two examples are given to show the effectiveness of the proposed synchronous solution method for the chaotic system tracking problem.We develop an optimal tracking control method for chaotic system with unknown dynamics and disturbances. The method allows the optimal cost function and the corresponding tracking control to update synchronously. According to the tracking error and the reference dynamics, the augmented system is constructed. Then the optimal tracking control problem is defined. The policy iteration （PI） is introduced to solve the rain-max optimization problem. The off-policy adaptive dynamic programming （ADP） algorithm is then proposed to find the solution of the tracking Hamilton-Jacobi- Isaacs （HJI） equation online only using measured data and without any knowledge about the system dynamics. Critic neural network （CNN）, action neural network （ANN）, and disturbance neural network （DNN） are used to approximate the cost function, control, and disturbance. The weights of these networks compose the augmented weight matrix, and the uniformly ultimately bounded （UUB） of which is proven. The convergence of the tracking error system is also proven. Two examples are given to show the effectiveness of the proposed synchronous solution method for the chaotic system tracking problem.

关 键 词：adaptive dynamic programming approximate dynamic programming chaotic system ZERO-SUM 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]