Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

doi:10.1088/1674-1056/20/11/110506

中国物理B ›› 2011, Vol. 20 ›› Issue (11): 110506-110506.doi: 10.1088/1674-1056/20/11/110506

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

杨世平¹, 张若洵²

(1)College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China; (2)College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China; College of Elementary Education, Xingtai University, Xingtai 054001, China

收稿日期:2011-05-27 修回日期:2011-06-30 出版日期:2011-11-15 发布日期:2011-11-15
基金资助:
Project supported by the Natural Science Foundation of Hebei Province, China (Grant No. A2010000343).

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

Zhang Ruo-Xun(张若洵)^a)b) and Yang Shi-Ping (杨世平)^a)^†

^a College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China; ^b College of Elementary Education, Xingtai University, Xingtai 054001, China

Received:2011-05-27 Revised:2011-06-30 Online:2011-11-15 Published:2011-11-15
Supported by:
Project supported by the Natural Science Foundation of Hebei Province, China (Grant No. A2010000343).

摘要/Abstract

摘要： In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

关键词: stabilization, modified adaptive feedback control, fractional-order chaotic system, chaos control

Abstract: In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

Key words: stabilization, modified adaptive feedback control, fractional-order chaotic system, chaos control

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

张若洵, 杨世平. Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller[J]. 中国物理B, 2011, 20(11): 110506-110506.

Zhang Ruo-Xun(张若洵) and Yang Shi-Ping (杨世平) . Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller[J]. Chin. Phys. B, 2011, 20(11): 110506-110506.

参考文献 24

[1]	Bagley R L, Calico R A and Guid J 1991 Control Dyn. 14 304
[2]	Sun H H, Abdelwahad A A and Onaral B 1984 IEEE Trans. Automat. Control 29 441
[3]	Ichise M, Nagayanagi Y and T Kojima 1971 J. Electroanal. Chem. 33 253
[4]	Heaviside O 1971 Electromagnetic (New York: Theory Chelsea)
[5]	Li C G and Chen G R 2004 Chaos Soliton. Fract. 22 549
[6]	Zhang R X and Yang S P 2009 Chin. Phys. B 18 3295
[7]	Lu J G 2005 Chaos Solition. Fract. 26 1125
[8]	Zhang R X and Yang S P 2009 Acta Phys. Sin. 58 2957 (in Chinese)
[9]	Deng W H and Li C P 2005 Physica A 353 61
[10]	Chen W C 2008 Chaos Soliton. Fract. 36 1305
[11]	Ahmad W M, El-Khazali R and Al-Assaf Y 2004 Chaos Soliton. Fract. 22 141
[12]	Ahmed E, El-Sayed A M A and El-Saka H A A 2006 Phys. Lett. A 358 1
[13]	Qi D L, Yang J and Zhang J L 2010 Chin. Phys. B 19 100506
[14]	Podlubny I Fractional Differential Equations 1999 (New York: Academic Press)
[15]	Li Y, Chen Y Q and Podlubny I 2010 Computers & Mathematics with Applications 59 1810
[16]	Carpinteri A and Mainardi F (ed.) 1997 Fractals and Fractional Calculus (New York: Springer)
[17]	Deng W H, Li C P and Lü J H 2007 Nonlinear Dyn. 48 409
[18]	Deng W H 2007 J. Comput. Phys. 227 1510
[19]	Lü J H, Chen G R, Cheng D Z and Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[20]	Deng W H and Li C P 2008 Phys. Lett. A 372 401
[21]	Wang M J and Wang X Y 2010 Acta Phys. Sin. 59 1583 (in Chinese)
[22]	Xu Z and Liu C X 2008 Chin. Phys. B 17 4033
[23]	Lu J G 2005 Chin. Phys. 14 1517
[24]	Hartley T T, Lorenzo C F and Qammer H K 1995 IEEE Trans. CAS-I 42 485

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

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