中国物理B ›› 2017, Vol. 26 ›› Issue (3): 30505-030505.doi: 10.1088/1674-1056/26/3/030505

• GENERAL • 上一篇    下一篇

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

Ruizhuo Song(宋睿卓), Qinglai Wei(魏庆来)   

  1. 1 School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
    2 The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
  • 收稿日期:2016-10-09 修回日期:2016-12-18 出版日期:2017-03-05 发布日期:2017-03-05
  • 通讯作者: Qinglai Wei E-mail:qinglai.wei@ia.ac.cn
  • 基金资助:
    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), and the Open Research Project from SKLMCCS, China (Grant No. 20150104).

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

Ruizhuo Song(宋睿卓)1, Qinglai Wei(魏庆来)2   

  1. 1 School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
    2 The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2016-10-09 Revised:2016-12-18 Online:2017-03-05 Published:2017-03-05
  • Contact: Qinglai Wei E-mail:qinglai.wei@ia.ac.cn
  • Supported by:
    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), and the Open Research Project from SKLMCCS, China (Grant No. 20150104).

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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 min-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

Abstract: 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 min-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.

Key words: adaptive dynamic programming, approximate dynamic programming, chaotic system, zero-sum

中图分类号:  (Control of chaos, applications of chaos)

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