Adaptive control of bifurcation and chaos in a time-delayed system

doi:10.1088/1674-1056/22/3/030508

Abstract In this paper, the stabilization of a continuous time-delayed system is considered. To control the bifurcation and chaos in a time-delayed system, a parameter perturbation control and a hybrid control are proposed. Then, to ensure the asymptotic stability of the system in the presence of unexpected system parameter changes, the adaptive control idea is introduced, i.e., the perturbation control parameter and the hybrid control parameter are automatically tuned according to the adaptation laws, respectively. The adaptation algorithms are constructed based on the Lyapunov–Krasovskii stability theorem. The adaptive parameter perturbation control and the adaptive hybrid control methods improve the corresponding constant control methods. They have the advantages of increased stability, adaptability to the changes of the system parameters, control cost saving, and simplicity. Numerical simulations for a well-known chaotic time-delayed system are performed to demonstrate the feasibility and superiority of the proposed control methods. Besides, comparison of the two adaptive control methods are made in an experimental study.

Keywords: delay parameter perturbation control hybrid control adaptive control

Received: 11 July 2012
Revised: 18 August 2012
Accepted manuscript online:

PACS:	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10772043), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090042110003), and the Science Research Project of Education Department of Liaoning Province, China (Grant No. L2012208).

Corresponding Authors: Yuan Hui-Qun
E-mail: yuan_hq@163.com

Cite this article:

Li Ning (李宁), Yuan Hui-Qun (袁惠群), Sun Hai-Yi (孙海义), Zhang Qing-Ling (张庆灵) Adaptive control of bifurcation and chaos in a time-delayed system 2013 Chin. Phys. B 22 030508

[1]	Dugard L and Verriest E I 1998 Stability and Control of Time-Delay Systems (London: Springer)
[2]	Gu K, Kharitonov V L and Chen J 2003 Stability of Time-Delay Systems (Boston: Birkhäuser)
[3]	Mackey M C and Glass L 1977 Science 197 287
[4]	Ye Z Y, Yang G and Deng C B 2011 Chin. Phys. B 20 010207
[5]	Zhao H Y, Yu X H and Wang L 2012 Int. J. Bifurcat. Chaos 22 1250036
[6]	Wang S L, Wang S L and Song X Y 2012 Nonlinear Dyn. 67 629
[7]	Zhao H Y and Xie W 2011 Nonlinear Dyn. 63 345
[8]	Balasubramaniam P, Kalpana M and Rakkiyappan R 2012 Chin. Phys. B 21 048402
[9]	Yang J H and Liu X B 2012 Acta Phys. Sin. 61 010505 (in Chinese)
[10]	Gong D W, Zhang H G and Wang Z S 2012 Chin. Phys. B 21 030204
[11]	Yu P, Yuan Y and Xu J 2002 Commun. Nonlinear Sci. Numer. Simulat. 7 69
[12]	Chen G and Yu X 1999 IEEE Trans. Circ. Sys. I 46 767
[13]	Luo X S, Fang J Q, Kong L J and Weng J Q 2000 Acta Phys. Sin. 49 1423 (in Chinese)
[14]	Peng J H, Tang J S, Yu D J, Hai W H and Yan J R 2003 Chin. Phys. 12 17
[15]	Yang L, Liu Z and Mao J 2000 Phys. Rev. Lett. 84 67
[16]	Yang L, Liu Z and Chen G 2002 Int. J. Bifurcat. Chaos 12 1411
[17]	Luo X S, Chen G R, Wang B H and Fang J Q 2003 Chaos Soliton. Fract. 18 775
[18]	Liu Z R and Chung K W 2005 Int. J. Bifurcat. Chaos 15 3895
[19]	Jimenez-Triana A, Tang W K S and Chen G R 2010 IEEE Trans. Circ. Sys. II 57 305
[20]	Wu Z M, Xie J Y, Fang Y Y and Xu Z Y 2007 Chaos Soliton. Fract. 32 104
[21]	Kavitha A and Uma G 2010 J. Electr. Eng. Technol. 5 171
[22]	Zhou Y F, Tse C K, Qiu S S and Chen J N 2005 Chin. Phys. 14 61
[23]	Wang T S, Wang X Y and Wang M J 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3367
[24]	Zhang L P, Wang H N and Xu M 2011 Acta Phys. Sin. 60 010506 (in Chinese)
[25]	Ding D W, Zhu J and Luo X S 2008 Chin. Phys. B 17 105
[26]	Liu F, Guan Z H and Wang H 2008 Chin. Phys. B 17 2405
[27]	Rezaie B and Motlagh M R J 2011 Nonlinear Dyn. 64 167
[28]	Jiang M, Shena Y, Jian J and Liao X 2006 Phys. Lett. A 350 221

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