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Chin. Phys. B, 2014, Vol. 23(5): 050504    DOI: 10.1088/1674-1056/23/5/050504
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A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

Song Rui-Zhuo (宋睿卓)a, Xiao Wen-Dong (肖文栋)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
Abstract  We develop an online adaptive dynamic programming (ADP) based optimal control scheme for continuous-time chaotic systems. The idea is to use the ADP algorithm to obtain the optimal control input that makes the performance index function reach an optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to achieve optimal control. In the ADP structure, neural networks are used to construct a critic network and an action network, which can obtain an approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Our simulation results illustrate the performance of the established optimal control method.
Keywords:  adaptive dynamic programming      adaptive critic designs      optimal control      continuous-time chaotic system  
Received:  18 October 2013      Revised:  16 November 2013      Accepted manuscript online: 
PACS:  05.45.Gg (Control of chaos, applications of chaos)  
Fund: Project supported by the Open Research Project from the 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), the National Natural Science Foundation of China (Grant Nos. 61304079 and 61374105), and the Natural Science Foundation of Beijing, China (Grant No. 4132078 and 4143065).
Corresponding Authors:  Wei Qing-Lai     E-mail:  ql_wei@126.com
About author:  05.45.Gg

Cite this article: 

Song Rui-Zhuo (宋睿卓), Xiao Wen-Dong (肖文栋), Wei Qing-Lai (魏庆来) A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm 2014 Chin. Phys. B 23 050504

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