Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

doi:10.1088/1674-1056/22/9/090502

中国物理B ›› 2013, Vol. 22 ›› Issue (9): 90502-090502.doi: 10.1088/1674-1056/22/9/090502

Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

宋睿卓^a, 肖文栋^a, 孙长银^a, 魏庆来^b

a School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
b 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:2012-12-06 修回日期:2013-03-25 出版日期:2013-07-26 发布日期:2013-07-26
基金资助:
Project supported by the Open Research Project from SKLMCCS (Grant No. 20120106), the Fundamental Research Funds for the Central Universities of China (Grant No. FRF-TP-13-018A), the Postdoctoral Science Foundation of China (Grant No. 2013M530527), and the National Natural Science Foundation of China (Grant Nos. 61304079, 61125306, and 61034002).

Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

Song Rui-Zhuo (宋睿卓)^a, Xiao Wen-Dong (肖文栋)^a, Sun Chang-Yin (孙长银)^a, Wei Qing-Lai (魏庆来)^b

a School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
b The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China

Received:2012-12-06 Revised:2013-03-25 Online:2013-07-26 Published:2013-07-26
Contact: Song Rui-Zhuo E-mail:ruizhuosong@163.com
Supported by:
Project supported by the Open Research Project from SKLMCCS (Grant No. 20120106), the Fundamental Research Funds for the Central Universities of China (Grant No. FRF-TP-13-018A), the Postdoctoral Science Foundation of China (Grant No. 2013M530527), and the National Natural Science Foundation of China (Grant Nos. 61304079, 61125306, and 61034002).

摘要/Abstract

摘要： In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming (ADP) algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.

关键词: chaotic systems, approximation error, adaptive dynamic programming, optimal tracking control

Abstract: In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming (ADP) algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.

Key words: chaotic systems, approximation error, adaptive dynamic programming, optimal tracking control

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

05.45.Gg

宋睿卓, 肖文栋, 孙长银, 魏庆来. Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof[J]. 中国物理B, 2013, 22(9): 90502-090502.

Song Rui-Zhuo (宋睿卓), Xiao Wen-Dong (肖文栋), Sun Chang-Yin (孙长银), Wei Qing-Lai (魏庆来). Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof[J]. Chin. Phys. B, 2013, 22(9): 90502-090502.

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Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

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