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Chin. Phys. B, 2012, Vol. 21(8): 080505    DOI: 10.1088/1674-1056/21/8/080505
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A single adaptive controller with one variable for synchronization of fractional-order chaotic systems

Zhang Ruo-Xun (张若洵)a b, 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
Abstract  In this paper we investigate the synchronization of a class of three-dimensional fractional-order chaotic systems. Based on Lyapunov stability theory and adaptive control technique, a single adaptive-feedback controller is developed to synchronize a class of fractional-order chaotic systems. The presented controller which only contains a single driving variable is simple both in design and in implementation. Numerical simulation and circuit experimental results for fractional-order chaotic system are provided to illustrate the effectiveness of the proposed scheme.
Keywords:  adaptive control      fractional-order chaotic system      a single controller  
Received:  04 December 2011      Revised:  28 January 2012      Accepted manuscript online: 
PACS:  05.45.Xt (Synchronization; coupled oscillators)  
Fund: Project supported by the Natural Science Foundation of Hebei Province, China (Grant No. A2010000343).
Corresponding Authors:  Yang Shi-Ping     E-mail:  yangship@mail.hebtu.edu.cn

Cite this article: 

Zhang Ruo-Xun (张若洵), Yang Shi-Ping (杨世平) A single adaptive controller with one variable for synchronization of fractional-order chaotic systems 2012 Chin. Phys. B 21 080505

[1] Bagley R L and Calico R A 1991 J. Guid. Control Dyn. 14 304
[2] Sun H H, Abdelwahad A A and Onaral B 1984 IEEE Trans. Autom. Control 29 441
[3] Ichise M, Nagayanagi Y and Kojima T 1971 J. Electroanal. Chem. Interfacial Electrochem 33 253
[4] Heaviside O 1971 Electromagnetic Theory (New York: Chelsea)
[5] Mandelbrot B and Van Ness J W 1968 SIAM Rev. 10 422
[6] Oustaloup A and La Derivation 1995 Non Entiere: Theorie, Synthase et Applications Editions Hermes, Paris, France
[7] Podlubny I 1999 IEEE Trans. Automat. Control 44 208
[8] Linares H, Baillot Ch, Oustaloup A and Ceyral Ch Generation of a Fractal Ground: Application in Robotics, in: International Congress in IEEE-SMC CESA'96 IMACS Multiconf., Lille, July 1996
[9] Duarte F B M and Macado J A T 2002 Nonlinear Dyn. 29 315
[10] Li C P and Deng W H 2006 Int. J. Mod. Phys. B 20 791
[11] Lu J G 2006 Physica A 359 107
[12] Wu X J, Lu H T and Shen S L 2009 Phys. Lett. A 373 2329
[13] Zhang R X and Yang S P 2010 Chin. Phys. B 19 020510
[14] Odibat Z M 2010 Nonlinear Dyn. 60 479
[15] Wang X Y, Zhang Y L, Lin D and Zhang N 2011 Chin. Phys. B 20 030506
[16] Tavazoei M S and Haeri M 2008 Physica A 387 57
[17] Zhang R X and Yang S P 2011 Nonlinear Dyn. 66 831
[18] Lu J G 2006 Chaos, Solitions and Fractals 27 519
[19] Wu C J, Zhang Y B and Yang N N 2011 Chin. Phys. B 20 060505
[20] Wang M J, Wang X Y and Niu Y J 2011 Chin. Phys. B 20 010508
[21] Qi D L,Yang J and Zhang J L 2010 Chin. Phys. B 19 100506
[22] Zhang R X and Yang S P 2011 Chin. Phys. B 20 090512
[23] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[24] Li Y, Chen Y Q and Podlubny I 2010 Comput. Math. Appl. 59 1810
[25] Hartley T T, Lorenzo C F and Qammer H K 1995 IEEE Trans CAS I 42 485
[26] Wang X J, Li J and Chen G R 2008 J. Franklin Institute 345 392
[27] Zhang R X and Yang S P 2009 Acta Phys. Sin. 58 2957 (in Chinese)
[28] Zhang R X and Yang S P 2009 Chin. Phys. B 18 3295
[29] Chen W C 2008 Chaos, Solitons and Fractals 36 1305
[30] Xu Z and Liu C X 2008 Chin. Phys. B 17 4033
[31] Lu J G 2005 Chin. Phys. 14 1517
[32] Qi G Y, Chen G R, Du S Z and Chen Z Q 2005 Physica A 352 295
[33] Song L, Yang J Y and Xu S Y 2010 Nonlinear Analysis: Theory Methods & Applications 72 2326
[34] Lu J G 2005 Chaos, Solitons and Fractals 26 1125
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