Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance

doi:10.1088/1674-1056/22/10/100504

中国物理B ›› 2013, Vol. 22 ›› Issue (10): 100504-100504.doi: 10.1088/1674-1056/22/10/100504

Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance

王东风, 张金营, 王晓燕

Hebei Engineering Research Center of Simulation & Optimized Control for Power Generation(North China Electric Power University), Baoding 071003, China

收稿日期:2013-03-04 修回日期:2013-04-15 出版日期:2013-08-30 发布日期:2013-08-30
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61203041) and the Fundamental Research Funds for the Central Universities of China (Grant No. 11MG49).

Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance

Wang Dong-Feng (王东风), Zhang Jin-Ying (张金营), Wang Xiao-Yan (王晓燕)

Hebei Engineering Research Center of Simulation & Optimized Control for Power Generation(North China Electric Power University), Baoding 071003, China

Received:2013-03-04 Revised:2013-04-15 Online:2013-08-30 Published:2013-08-30
Contact: Zhang Jin-Ying E-mail:k.ying_zhang@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61203041) and the Fundamental Research Funds for the Central Universities of China (Grant No. 11MG49).

摘要/Abstract

摘要： Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance. Simulation of the fractional-order Lorenz chaotic system and fractional-order Chen’s chaotic system with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.

关键词: fractional-order chaotic system, modified projective synchronization, uncertainty, disturbance

Abstract: Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance. Simulation of the fractional-order Lorenz chaotic system and fractional-order Chen’s chaotic system with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.

Key words: fractional-order chaotic system, modified projective synchronization, uncertainty, disturbance

中图分类号: (Control of chaos, applications of chaos)

05.45.Gg

05.45.Xt (Synchronization; coupled oscillators) 05.45.Pq (Numerical simulations of chaotic systems)

王东风, 张金营, 王晓燕. Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance[J]. 中国物理B, 2013, 22(10): 100504-100504.

Wang Dong-Feng (王东风), Zhang Jin-Ying (张金营), Wang Xiao-Yan (王晓燕). Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance[J]. Chin. Phys. B, 2013, 22(10): 100504-100504.

参考文献 45

[1]	Bagley R L and Calico R A 2012 Journal of Guidance, Control, and Dynamics 14 304
[2]	Ichise M, Nagayanagi Y and Kojima T 1971 J. Electroanal. Chem. Interfacial Electrochem. 33 253
[3]	Ezzat M A 2011 Appl. Math. Mod. 35 4965
[4]	Laskin N 2000 Physica A 287 482
[5]	Sun H, Abdelwahab A and Onaral B 1984 IEEE Trans. Autom. Control 29 441
[6]	Podlubny I 1999 Fractional Differential Equation (New York: Academic Press) pp. 41-48, 71
[7]	Vinagre B M, Podlubny I, Hernandez A and Feliu V 2000 Fractional Calculus and Applied Analysis 3 231
[8]	Yang Q G and Zeng C B 2010 Commun. Nonlinear Sci. Numer. Simul. 15 4041
[9]	Ge Z M and Ou C Y 2007 Chaos, Solitons and Fractals 34 262
[10]	Zhu H, Zhou S B and Zhang J 2009 Chaos, Solitons and Fractals 39 1595
[11]	Lu J G and Chen G R 2006 Chaos, Solitons and Fractals 27 685
[12]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[13]	Aghababa M P and Akbari M E 2012 Appl. Math. Comput. 218 5757
[14]	Wei W, Li D H and Wang J 2010 Chin. Phys. B 19 040507
[15]	Pourgholi M and Majd V J 2011 Chin. Phys. B 20 120503
[16]	Duan Z S and Chen G R 2012 Chin. Phys. B 21 080506
[17]	Zhao L, Liao X F, Xiang T and Xiao D 2009 Chin. Phys. Lett. 26 060502
[18]	Wang Z, Huang X, Li N and Song X N 2012 Chin. Phys. B 21 050506
[19]	Dong E Z, Chen Z Q, Chen Z P and Ni J Y 2012 Chin. Phys. B 21 030501
[20]	Hua C C and Guan X P 2004 Chin. Phys. Lett. 21 1441
[21]	Pei W, Lü J H and Ogorzalek M J 2012 Neurocomputing 78 155
[22]	Chen Y, Lü J H and Lin Z 2013 Automatica (http://dx.doi.org/10.1016/j.automatica. 2013.02.021.)
[23]	Zhu J D, Lü J H and Yu X H 2013 IEEE Trans. Circ. Syst. Regul. Pap. 60 199
[24]	Lü J H, Yu X H, Chen G R and Cheng D Z 2004 IEEE Trans. Circ. Syst. Regul. Pap. 51 787
[25]	Lü J H and Chen G R 2005 IEEE Trans. Autom. Control 50 841
[26]	Liu H, Lu J A, Lü J H and Hill D J 2009 Automatica 45 1799
[27]	Zhou J, Lu J A and Lü J H 2006 IEEE Trans. Autom. Control 51 652
[28]	Wang Z, Huang X and Zhao Z 2012 Nonlinear Dyn. 69 999
[29]	Wang X Y, Zhang X P and Ma C 2012 Nonlinear Dyn. 69 511
[30]	Chen L P, Wei S B, Chai Y and Wu R C 2012 Math. Probl. Eng. 2012 1
[31]	Martinez-Martinez R, Mata-Machuca J L, Martinez-Guerra R, Leon J A and Fernandez-Anaya G 2011 Appl. Math. Comput. 218 3338
[32]	Zheng S 2012 Appl. Math. Comput. 218 5891
[33]	Xu J Q Proceedings of the 30th Chinese Control Conference, July 22-24, 2011, Yantai, China, pp. 2423-2428
[34]	Zhou P and Ding R 2012 Indian J. Phys. 86 497
[35]	Yang C C 2012 J. Franklin Inst. 349 349
[36]	Zhang R X and Yang S P 2012 Nonlinear Dyn. 69 983
[37]	Xiang W and Chen F Q 2011 Commun. Nonlinear Sci. Numer. Simul. 16 2970
[38]	Li G H 2007 Chaos, Solitons and Fractals 32 1786
[39]	Li Y, Chen Y Q and Podlubny I 2010 Comput. Math. Appl. 59 1810
[40]	Ye M Y 2005 Acta Phys. Sin. 54 30 (in Chinese)
[41]	Li C P and Yan J P 2007 Chaos, Solitons and Fractals 32 751
[42]	Caponetto R, Dongola G and Fortuna L 2010 Fractional Order Systems: Modeling and Control Applications (Hackensack: World Scientific) p. 62
[43]	Li C G and Chen G R 2004 Chaos, Solitons and Fractals 22 549
[44]	Chen G R and Ueta T 1999 Int. J. Bifur. Chaos Appl. Sci. Eng. 9 1465
[45]	Chen Y, Lü J H and Yu X H 2011 Sci. China: Technol. Sci. 54 2014

Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance

Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance

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