Synchronization of uncertain fractional-order chaotic systems with disturbance based on fractional terminal sliding mode controller

doi:10.1088/1674-1056/22/4/040507

Abstract This paper provides a novel method to synchronize the uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on the Lyapunov stability theory, a new fractional-order switching manifold is proposed and in order to ensure the occurrence of the sliding motion in finite time, the corresponding sliding mode control law is designed. The proposed control scheme is applied to synchronizing the fractional-order Lorenz chaotic system and fractional-order Chen's chaotic system with parameters uncertainty and external disturbance. Simulation results show the applicability and the efficiency of the proposed scheme.

Keywords: fractional-order chaotic system synchronization terminal sliding mode control uncertainty disturbance

Received: 23 August 2012
Revised: 17 October 2012
Accepted manuscript online:

PACS:	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.Xt	(Synchronization; coupled oscillators)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 11MG49).

Corresponding Authors: Zhang Jin-Ying
E-mail: k.ying zhang@163.com

Cite this article:

Wang Dong-Feng (王东风), Zhang Jin-Ying (张金营), Wang Xiao-Yan (王晓燕) Synchronization of uncertain fractional-order chaotic systems with disturbance based on fractional terminal sliding mode controller 2013 Chin. Phys. B 22 040507

[1]	Watts D J and Strogatz S H 1998 Nature 393 440
[2]	Barabási A L and Albert R 1999 Science 286 509
[3]	Lü J H and Chen G R 2005 IEEE Trans. Autom. Control 50 841
[4]	Liu H, Lu J A, Lü J H and Hill D J 2009 Automatica 45 1799
[5]	Duan Z S and Chen G R 2012 Chin. Phys. B 21 080506
[6]	Lü J H, Yu X H, Chen G R and Cheng D Z 2004 IEEE Trans. Circ. Sys. I: Regular Papers 51 787
[7]	He D R, Liu Z H and Wang B H 2009 Complex Systems and Complex Networks (Beijing: Higher Education Press) pp. 1-4 (in Chinese)
[8]	Zhou J, Lu J A and Lü J H 2006 IEEE Trans. Autom. Control 51 652
[9]	Zhao L, Liao X F, Xiang T and Xiao D 2009 Chin. Phys. Lett. 26 060502
[10]	Wang Z, Huang X, Li N and Song X N 2012 Chin. Phys. B 21 050506
[11]	Dong E Z, Chen Z Q, Chen Z P and Ni J Y 2012 Chin. Phys. B 21 030501
[12]	Hua C C and Guan X P 2004 Chin. Phys. Lett. 21 1441
[13]	Pei W, Lü J H and Ogorzalek M J 2012 Neurocomputing 78 155
[14]	Hu K X and Zhu K Q 2009 Chin. Phys. Lett. 26 108301
[15]	Ichise M, Nagayanagi Y and Kojima T 1971 J. Electroanal. Chem. Interfacial Electrochem. 33 253
[16]	Ezzat M A 2011 Appl. Math. Modelling 35 4965
[17]	Laskin N 2000 Physica A 287 482
[18]	Sun H, Abdelwahab A and Onaral B 1984 IEEE Trans. Autom. Control 29 441
[19]	Podlubny I 1999 Fractional Differential Equation (New York: Academic Press) pp. 41-48, 71.
[20]	Vinagre B M, Podlubny I, Hernandez A and Feliu V 2000 Fractional Calculus and Applied Analysis 3 231
[21]	Si G Q, Sun Z Y and Zhang Y B 2011 Chin. Phys. B 20 080505
[22]	Ge Z M and Ou C Y 2007 Chaos, Solitons and Fractals 34 262
[23]	Zhu H, Zhou S B and Zhang J 2009 Chaos, Solitons and Fractals 39 1595
[24]	Lu J G and Chen G R 2006 Chaos, Solitons and Fractals 27 685
[25]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[26]	Zhang Q L and Lu L 2011 Chin. Phys. B 20 010510
[27]	Wei W, Li D H and Wang J 2010 Chin. Phys. B 19 040507
[28]	Pourgholi M and Majd V J 2011 Chin. Phys. B 20 120503
[29]	Hu A H, Xu Z Y and Guo L X 2011 Chin. Phys. B 20 090511
[30]	Zhang R X and Yang S P 2012 Chin. Phys. B 21 030505
[31]	Fu J, Yu M and Ma T D 2011 Chin. Phys. B 20 120508
[32]	Jia L X, Dai H and Hui M 2010 Chin. Phys. B 19 110509
[33]	Wang S and Yu Y G 2012 Chin. Phys. Lett. 29 020505
[34]	Xu J Q Proceedings of the 30th Chinese Control Conference, July 22-24, 2011, Yantai, China, p. 2423
[35]	Zhou P and Ding R 2012 Indian J. Phys. 86 497
[36]	Yang C C 2012 J. Franklin Inst. 349 349
[37]	Zhang R X and Yang S P 2012 Nonlinear Dyn. 69 983
[38]	Xiang W and Chen F Q 2011 Commun. Nonlinear Sci. Numer. Simul. 16 2970
[39]	Dadras S and Momeni H R 2012 Commun. Nonlinear Sci. Numeri. Simul. 17 367
[40]	Qi D L, Wang Q and Yang J 2011 Chin. Phys. B 20 100505
[41]	Zhang H and Pu Q M Proceedings of the 2011 International Conference on Engineering Materials, Energy, Management and Control, January 22-23, 2011, Beijing, China, p. 723
[42]	Yin C, Zhong S M and Chen W F 2012 Commun. Nonlinear Sci. Numer. Simul. 17 356
[43]	Tarasov V E 2007 Int. J. Math. 18 281
[44]	Kilbas A A, Srivastava H M and Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier Ltd.) p. 72
[45]	Samko S G, Kilbas A A and Marichev O I 1993 Fractional Integrals and Derivatives: Theory and Applications (Switzerland: Gordon and Breach Science Publishers) pp. 48, 49, 66, 67
[46]	Khalil H K 2002 Nonlinear Systems 3nd edn. (London: Prentice Hall) p. 144
[47]	Li Y, Chen Y Q and Podlubny I 2010 Comput. Math. Appl. 59 1810
[48]	Zak M 1988 Phys. Lett. A 133 18
[49]	Man Z H, Paplinski A P and Wu H R 1994 IEEE Trans. Autom. Control 39 2464
[50]	Man Z H and Yu X H 1997 IEEE Trans. Circ. Sys. I: Fundamental Theory and Applications 44 1065
[51]	Iglesias W J, Xu L and Saito O Proceedings of the 35th Conference on Decision and Control, December 11-13, 1996, Kobe, Japan, p. 4607
[52]	Li C P and Yan J P 2007 Chaos, Solitons and Fractals 32 751
[53]	Caponetto R, Dongola G and Fortuna L 2010 Fractional Order Systems: Modeling and Control Applications (Hackensack: World Scientific) p. 62
[54]	Li C G and Chen G R 2004 Chaos, Solitons and Fractals 22 549
[55]	Chen G R and Ueta T 1999 Int. J. Bifur. Chaos Appl. Sci. Eng. 9 1465
[56]	Yang Q G and Zeng C B 2010 Commun. Nonlinear Sci. Numer. Simul. 15 4041
[57]	Sang J Y, Yang J and Yue L J 2011 Chin. Phys. B 20 080507

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Synchronization of uncertain fractional-order chaotic systems with disturbance based on fractional terminal sliding mode controller

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