A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

doi:10.1088/1674-1056/23/5/050504

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

[1]	Liu S and Chen L 2013 Chin. Phys. B 22 100506
[2]	Feng J, Zhang Q, Wang W and Hao S 2013 Chin. Phys. B 22 090503
[3]	Luo Y and Du M 2013 Chin. Phys. B 22 080503
[4]	Giuseppe G 2013 Chin. Phys. B 22 080505
[5]	Chen S and Lu J 2002 Chaos Soliton. Fract. 14 643
[6]	Zhang H, Huang W, Wang Z, Wang a and Chai T 2006 Phys. Lett. A 350 363
[7]	Ma T and Fu J 2011 Chin. Phys. B 20 050511
[8]	Ma T, Fu J and Sun Y 2010 Chin. Phys. B 19 090502
[9]	Zhang H, Ma T, Fu J and Tong S 2009 Chin. Phys. B 18 3751
[10]	Ma T, Zhang H and Fu J 2008 Chin. Phys. B 17 4407
[11]	Zhang H, Wang Z and Liu D 2004 Int. J. Bifur. Chaos 14 3505
[12]	Song R, Xiao W, Sun C and Wei Q 2013 Chin. Phys. B 22 090502
[13]	Werbos P 1977 General Systems Yearbook 22 25
[14]	Zhang H, Song R, Wei Q and Zhang T 2011 IEEE Trans. Neural Netw. 22 1851
[15]	Zhang H, Wei Q and Liu D 2011 Automatica 47 207
[16]	Liu D and Wei Q 2013 Automatica
[17]	Zhang H, Wei Q and Luo Y 2008 IEEE Trans. Syst. Man Cybernet. B 38 937
[18]	Song R, Zhang H, Luo Y and Wei Q 2010 Neurocomputing 73 3020
[19]	Song R, Xiao W and Sun C 2013 Acta Automatica Sinica 39 1413
[20]	Song R, Xiao W and Zhang H 2013 Neurocomputing 119 212
[21]	Murray J, Cox C, Lendaris G and Saeks R 2002 IEEE Trans. Syst. Man Cybernet. C 32 140
[22]	Fu J, He H and Zhou X 2011 IEEE Trans. Neural Netw. 22 1133
[23]	Lewis F and Vamvoudakis K 2011 IEEE Trans. Syst. Man Cybernet. B 41 14
[24]	Zhang H and Lewis F 2012 Automatica 48 1432
[25]	Khalil H 2002 Nonlinear System (NJ: Prentice-Hall)
[26]	Vamvoudakis K and Lewis F 2010 Automatica 46 878

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