Adaptive lag synchronization of uncertain dynamical systems with time delays via simple transmission lag feedback

doi:10.1088/1674-1056/22/8/080507

Abstract In this paper we present an adaptive scheme to achieve lag synchronization for uncertain dynamical systems with time delays and unknown parameters. In contrast to the nonlinear feedback scheme reported in the previous literature, the proposed controller is a linear one which only involves simple feedback information from the drive system with signal propagation lags. Besides, the unknown parameters can also be identified via the proposed updating laws in spite of the existence of model delays and transmission lags, as long as the linear independence condition between the related function elements is satisfied. Two examples, i.e., the Mackey-Glass model with single delay and the Lorenz system with multiple delays, are employed to show the effectiveness of this approach. Some robustness issues are also discussed, which shows that the proposed scheme is quite robust in switching and noisy environment.

Keywords: adaptive feedback time delay lag synchronization parameter identification noise perturbation

Received: 13 November 2012
Revised: 16 January 2013
Accepted manuscript online:

PACS:	05.45.Tp	(Time series analysis)
	05.45.Xt	(Synchronization; coupled oscillators)

Fund: Project supported by the National Science and Technology Major Project, China (Grant No. 2011ZX03005-002), the Shandong Academy of Science Development Fund for Science and Technology, China, and the Pilot Project for Science and Technology in Shandong Academy of Sciences, China.

Corresponding Authors: Sun Zhi-Yong
E-mail: kfmuzik@126.com, sun.zhiyong.cn@gmail.com, sunzhy@sdas.org

Cite this article:

Gu Wei-Dong (顾卫东), Sun Zhi-Yong (孙志勇), Wu Xiao-Ming (吴晓明), Yu Chang-Bin (于长斌) Adaptive lag synchronization of uncertain dynamical systems with time delays via simple transmission lag feedback 2013 Chin. Phys. B 22 080507

[1]	Pikovsky A, Rosenblum M and Kurths J 2003 Synchronization: A Universal Concept in Nonlinear Sciences (New York: Cambridge University Press)
[2]	Kapitaniak M, Czolczynski K, Perlikowski P, Stefanski A and Kapitaniak T 2012 Phys. Rep. 517 1
[3]	Feng J, Yam P, Austin F and Xu C 2011 Zeitschrift fur Naturforschung A 66 6
[4]	Lu J, Kurths J, Cao J, Mahdavi N and Huang C 2012 IEEE Trans. Neural Netw. Learning System 23 285
[5]	Boccaletti S, Kurths J, Osipov G, Valladares D and Zhou C 2002 Phys. Rep. 366 1
[6]	Rosenblum M G, Pikovsky A S and Kurths J 1997 Phys. Rev. Lett. 78 4193
[7]	Wang D, Zhong Y and Chen S 2008 Commun. Nonlinear Sci. Numer. Simul. 13 637
[8]	Feng J, Dai A, Xu C and Wang J 2011 Comput. Math. Appl. 61 2123
[9]	Lü L and Li Y 2009 Acta Phys. Sin. 58 131 (in Chinese)
[10]	Liu H, Jun Y H and Wei X 2012 Acta Phys. Sin. 61 180503 (in Chinese)
[11]	Wang Q Y, Lu Q S and Duan Z S 2010 Int. J. Non-Linear Mech. 45 640
[12]	Sun Z and Yang X 2011 Chaos 21 033114
[13]	Chai Y and Chen L Q 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3390
[14]	Tang M 2012 Chin. Phys. B 21 020509
[15]	Huang Y, Zhang H and Wang Z 2012 Chin. Phys. B 21 070701
[16]	Wang S and Yao H 2012 Chin. Phys. B 21 050508
[17]	Shahverdiev E, Sivaprakasam S and Shore K 2002 Phys. Lett. A 292 320
[18]	Li C, Liao X and Wong K 2004 Physica D 194 187
[19]	Xu Y, Zhou W, Fang J and Sun W 2010 Phys. Lett. A 374 3441
[20]	Liu H, Lu J and Zhang Q 2010 Nonlinear Dyn. 62 427
[21]	Zhang R X and Yang S P 2011 Chin. Phys. B 20 090512
[22]	Yu W and Cao J 2007 Physica A 375 467
[23]	Pourdehi S, Karimaghaee P and Karimipour D 2011 Phys. Lett. A 375 1769
[24]	Liu H, Lu J A, Lü J and Hill D J 2009 Automatica 45 1799
[25]	Che Y, Li R, Han C, Wang J, Cui S, Deng B and Wei X 2012 Eur. Phys. J. B 85 1
[26]	Sun Z Y, Si G Q, Min F H and Zhang Y B 2012 Nonlinear Dyn. 68 471
[27]	Boyd S, El Ghaoul L, Feron E and Balakrishnan V 1987 Linear Matrix Inequalities in System and Control Theory (Philadephia: SIAM)
[28]	Ioannou P A and Sun J 1996 Robust Adaptive Control (Upper Saddle River, NJ: Prentice Hall)
[29]	Sun F, Peng H, Luo Q, Li L and Yang Y 2009 Chaos 19 23109
[30]	Zhao J C, Li Q, Lu J A and Jiang Z P 2010 Chaos 20 023119
[31]	Huang D 2005 Phys. Rev. E 71 037203
[32]	Huang D 2006 Phys. Rev. E 73 066204
[33]	Mackey M C and Glass L 1977 Science 197 287

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Adaptive lag synchronization of uncertain dynamical systems with time delays via simple transmission lag feedback

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