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浙江大学学报(工学版)
J4  2010, Vol. 44 Issue (7): 1288-1291    DOI: 10.3785/j.issn.1008-973X.2010.07.010
    
Projective synchronization of uncertain fractional order chaotic system using sliding mode controller
SUN Ning, ZHANG Huaguang, WANG Zhiliang
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Abstract  

A sliding mode controller was proposed for the projective synchronization of secondorder fractional uncertain chaotic system. The Caputo’s fractional derivative was adopted. The total controller was composed of the approach controller and the equivalence controller. The exponent approach law was adopted for the approach controller. The equivalence controller was designed by using of the fact that the time derivative of the sliding surface is zero when the trajectory of the controlled system is on the surface. The existence of the sliding surface was analyzed and a simple stability analysis was obtained based on the Lyapunov theory for fractional differential system. Then the stability theorem for fractional system considering the uncertainty was provided and the synchronization aim was achieved. The simulation for the fractional chaotic uncertain DuffingHolmes system showed the effectiveness of the controller.

Published: 01 July 2010
CLC:  TP 273  
  TP 29  
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Cite this article:

SUN Ning, ZHANG Hua-Guang, WANG Zhi-Liang. Projective synchronization of uncertain fractional order chaotic system using sliding mode controller. J4, 2010, 44(7): 1288-1291.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2010.07.010     OR     http://www.zjujournals.com/eng/Y2010/V44/I7/1288


不确定分数阶混沌系统的滑模投影同步

针对2阶不确定分数阶混沌系统的投影同步问题,提出基于滑模原理的同步控制方法.分数阶导数采用Caputo的定义.控制律由趋近控制和等价控制2部分组成.趋近控制采用指数趋近律,等价控制利用系统轨迹在滑模面上运动时滑模面的时间导数为零的条件得到.在控制器设计过程中,利用分数阶系统的Lyapunov理论分析滑模面的存在性,简化稳定性证明方法,得到了存在不确定性时分数阶系统达到同步的稳定性定理,实现了控制目标.通过对分数阶DuffingHolmes系统的完全状态投影同步的仿真,证明了该方法的有效性.

［1］ ZHU Weiguo, BAI Xiangzhong. Bifurcation and chaos of a 4side fixed rectangular thin plate in electromagnetic and mechanical fields ［J］. Jouranl of Zhejiang University: Science A, 2009, 10(1): 6271.

［2］ PECORA L M, CARROLL T L. Synchronization in chaotic systems ［J］. Physical Review Letters, 1990, 64(8): 821824.

［3］ ZHENG Qiang, ZHANG Xiaoping, REN Zhongzhou. Antisynchronization between Lorenz and Liu hyperchaotic systems ［J］. Communications in Theoretical Physics, 2008, 50(3): 677680.

［4］ ZHANG Huaguang, MA Tiedong, YU Wen, et al. A practical approach to robust impulsive lag synchronization between different chaotic systems ［J］. Chinese Physics B, 2008, 17(10): 36163622.

［5］ BOWONG S, MOUKAM KAKMENI F M, DIMI J L, et al. Synchronizing chaotic dynamics with uncertainties using a predictable synchronization delay design ［J］. Communications in Nonlinear Science and Numerical Simulation, 2006, 11(8): 973987.

［6］ 王兴元,贺毅杰.分数阶统一混沌系统的投影同步［J］.物理学报,2008,3: 14851492.

WANG Xingyuan, HE Yijie. Projective synchronization of the fractional order unified system ［J］. Acta Physica Sinica, 2008, 57(3): 14851492.

［7］ MAINIERI R, REHACEK J. Projective synchronization in threedimensional chaotic systems ［J］. Physical Review Letters, 1999, 82(15): 30423045.

［8］ LU Junguo. Chaotic dynamics and synchronization of fractionalorder Chua’s circuits with a piecewiselinear nonlinearity ［J］. International Journal of Modern Physics B, 2005, 19(20): 32493259.

［9］ LI Chunguang, CHEN Guanrong. Chaos in the fractional order Chen system and its control ［J］. Chaos, Solitons and Fractals, 2004, 22(3): 549554.

［10］ LU Junguo. Chaotic dynamics of the fractionalorder Lu system and its synchronization ［J］. Physics Letters A, 2006, 354(4):305311.

［11］ SHAO Shiquan. Controlling general projective synchronization of fractional order Rossler systems ［J］. Chaos, Solitons and Fractals, 2009, 39(4): 15721577.

［12］ 宋超,朱涛.半线性中立型发展方程mild解的存在性［J］.浙江大学学报:理学版,2010,37(1): 14.

SONG Chao, ZHU Tao. Existence of mild solutions to semilinear neutral evolution equations ［J］. Journal of Zhejiang University: Science Edition, 2010, 37(1): 14.


［13］ 程丽.不精确分式规划的一种有效算法［J］.浙江大学学报:理学版,2009,36(5): 503507.

CHENG Li. The efficient algorithm for inexact fractional programming ［J］. Journal of Zhejiang University: Science Edition, 2009, 36(5): 503507.

［14］ 王宣银,程佳.4TPS1PS四自由度并联电动平台动力学建模与位姿闭环鲁棒控制［J］.浙江大学学报:工学版,2009,43(8): 14921496.

WANG Xuanyin, CHENG Jia. Dynamic modeling and robust control in task space of 4DOF parallel electric platform with 4TPS1PS structure ［J］. Journal of Zhejiang University: Engineering Science, 2009, 43(8): 14921496.

［15］ 李强,王宣银,程佳.Stewart液压平台轨迹跟踪自适应滑模控制［J］.浙江大学学报:工学版,2009,43(6): 11241128.

LI Qiang, WANG Xuanyin, CHENG Jia. Adaptive slidingmode trajectorytracking control of hydraulic Stewart platform ［J］. Journal of Zhejiang University: Engineering Science, 2009, 43(6): 11241128.

［16］ 白寒,管成,潘双夏.基于模糊决策的推土机滑模鲁棒自适应控制［J］.浙江大学学报:工学版,2009, 43(12): 21782184.

BAI Han, GUAN Cheng, PAN Shuangxia. Fuzzy decision based sliding mode robust adaptive control for bulldozer ［J］. Journal of Zhejiang University: Engineering Science, 2009, 43(12): 21782184.

［17］ 颜闽秀,井元伟.基于终端滑模控制的混沌系统的同步［J］.东北大学学报：自然科学版,2007,28(12): 16771680.

YAN Minxiu, JING Yuanwei. Synchronization of chaotic systems using terminal sliding mode control ［J］. Journal of Northeastern University: Natural Science, 2007, 28(12): 16771680.

［18］ 王兴元,刘明.用滑模控制方法实现具有扇区非线性输入的主从混沌系统同步［J］.物理学报,2005,54(6): 25842589.

WANG Xingyuan, LIU Ming. Sliding mode control for the synchronization of masterslave chaotic systems with sector nonlinear input ［J］. Acta Physica Sinica, 2005, 54(6): 25842589.

［19］ MOHAMMAD S T, MOHAMMAD H. Synchronization of chaotic fractionalorder systems via active sliding mode controller ［J］. Physica AStatistical Mechanics and Its Applications, 2008, 387(1): 5770.

［20］ HOSSEINNIA S H, GHADERI R, RANJBAR N A, et al. Sliding mode synchronization of an uncertain fractional order chaotic system ［J］. Computers and Mathematics with Applications, 2010, 59(5): 16371643.

［21］ PODLUBNY I. Fractional differential equations ［M］. San Diego: Academic Press, 1999: 6286.

［22］ LI Yan, CHEN Yangquan, PODLUBNY I. MittagLeffler stability of fractional order nonlinear dynamic systems ［J］. Automatica, 2009, 45(8): 19651969.
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