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基于最小二乘支持向量机的分数阶混沌系统控制

阎晓妹 刘丁

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基于最小二乘支持向量机的分数阶混沌系统控制

阎晓妹, 刘丁

Control of fractional order chaotic system based on least square support vector machines

Yan Xiao-Mei, Liu Ding
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  • 提出了基于最小二乘支持向量机(LS-SVM)的分数阶混沌系统控制方法.基于分数阶线性系统稳定理论,通过线性分离的方法将系统分解为稳定的线性部分和相应的非线性部分,再利用支持向量机良好的非线性函数逼近和泛化能力设计了主动控制器,对非线性部分进行补偿,从而将分数阶混沌系统控制到平衡点.分别以分数阶Liu系统和分数阶Chen系统为例进行了仿真研究,表明该方法是有效和可行的.
    A new method based on least square support vector machines (LS-SVM) is proposed for chaos control of fractional order system. Based on the stability theory of fractional order linear system, the system is decomposed into stable linear parts and the corresponding nonlinear parts. The active controller is designed to compensate the nonlinear parts by using the excellent nonlinearity approximation ability and better generalization capacity of LS-SVM. Thus fractional order chaotic system is suppressed to the equilibrium point. Fractional order Liu system and fractional order Chen system are illustrated respectively. The simulation results verify the effectiveness and feasibility of the proposed method.
    • 基金项目: 国家自然科学基金(批准号:60804040)资助的课题.
    [1]

    [1]Bagley R L, Calico R A 1991 J. Guid. Control Dyn. 14 304

    [2]

    [2]Sun H H, Abdelwahad A A, Onaral B 1984 IEEE Trans.Automat. Control. 29 441

    [3]

    [3]Ichise M, Nagayanagi Y, Kojima T 1971 J. Electro-Anal.Chem. 33 253

    [4]

    [4]Li C P, Peng G J 2004 Chaos Soliton. Fract. 22 443

    [5]

    [5]Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101

    [6]

    [6]Ge Z M, Ou C Y 2007 Chaos Soliton. Fract. 34 262

    [7]

    [7]Lu J G 2006 Phys. Lett. A 354 305

    [8]

    [8]Liu C X 2007 Acta Phys. Sin. 56 6865 (in Chinese) [刘崇新 2007 物理学报 56 6865]

    [9]

    [9]Li C G, Chen G R 2004 Chaos Soliton. Fract. 22 549

    [10]

    ]Gao X, Yu J B 2005 Chin. Phys. 14 908

    [11]

    ]Zhang C F, Gao J F, Xu L 2007 Acta Phys. Sin. 56 5124 (in Chinese) [张成芬、高金峰、徐磊 2007 物理学报 56 5124]

    [12]

    ]Zhong Q S, Bao J F, Yu Y B, Liao X F 2009 Chin. Phys. Lett. 25 2812

    [13]

    ]Vapnik V N 2000 The nature of statistical learning theory (2nd ed) (New York: Springer-Vedag) p125

    [14]

    ]Suykens J A K, Vandewalle J 1999 Int. J. Circ. Theor. Appl. 27 605

    [15]

    ]Ye M Y 2005 Acta Phys. Sin. 54 30 (in Chinese) [叶美盈 2005 物理学报 54 30 ]

    [16]

    ]Liu H, Liu D, Ren H P 2005 Acta Phys. Sin. 54 4019 (in Chinese) [刘涵、刘丁、任海鹏 2005 物理学报 54 4019]

    [17]

    ]Podlubny I 1999 Fractional differential equations (1st ed) (New York: Academic Press) p41

    [18]

    ]Matignon D 1996 IMACS- SMC Proceedings, Lille, France, July, 1996 p963

    [19]

    ]Ahmed E, El-Sayed A M A, El-Saka H A A 2007 J. Math. Anal. Appl. 325 542

  • [1]

    [1]Bagley R L, Calico R A 1991 J. Guid. Control Dyn. 14 304

    [2]

    [2]Sun H H, Abdelwahad A A, Onaral B 1984 IEEE Trans.Automat. Control. 29 441

    [3]

    [3]Ichise M, Nagayanagi Y, Kojima T 1971 J. Electro-Anal.Chem. 33 253

    [4]

    [4]Li C P, Peng G J 2004 Chaos Soliton. Fract. 22 443

    [5]

    [5]Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101

    [6]

    [6]Ge Z M, Ou C Y 2007 Chaos Soliton. Fract. 34 262

    [7]

    [7]Lu J G 2006 Phys. Lett. A 354 305

    [8]

    [8]Liu C X 2007 Acta Phys. Sin. 56 6865 (in Chinese) [刘崇新 2007 物理学报 56 6865]

    [9]

    [9]Li C G, Chen G R 2004 Chaos Soliton. Fract. 22 549

    [10]

    ]Gao X, Yu J B 2005 Chin. Phys. 14 908

    [11]

    ]Zhang C F, Gao J F, Xu L 2007 Acta Phys. Sin. 56 5124 (in Chinese) [张成芬、高金峰、徐磊 2007 物理学报 56 5124]

    [12]

    ]Zhong Q S, Bao J F, Yu Y B, Liao X F 2009 Chin. Phys. Lett. 25 2812

    [13]

    ]Vapnik V N 2000 The nature of statistical learning theory (2nd ed) (New York: Springer-Vedag) p125

    [14]

    ]Suykens J A K, Vandewalle J 1999 Int. J. Circ. Theor. Appl. 27 605

    [15]

    ]Ye M Y 2005 Acta Phys. Sin. 54 30 (in Chinese) [叶美盈 2005 物理学报 54 30 ]

    [16]

    ]Liu H, Liu D, Ren H P 2005 Acta Phys. Sin. 54 4019 (in Chinese) [刘涵、刘丁、任海鹏 2005 物理学报 54 4019]

    [17]

    ]Podlubny I 1999 Fractional differential equations (1st ed) (New York: Academic Press) p41

    [18]

    ]Matignon D 1996 IMACS- SMC Proceedings, Lille, France, July, 1996 p963

    [19]

    ]Ahmed E, El-Sayed A M A, El-Saka H A A 2007 J. Math. Anal. Appl. 325 542

计量
  • 文章访问数:  4560
  • PDF下载量:  917
  • 被引次数: 0
出版历程
  • 收稿日期:  2009-08-25
  • 修回日期:  2009-11-13
  • 刊出日期:  2010-05-15

基于最小二乘支持向量机的分数阶混沌系统控制

  • 1. 西安理工大学自动化与信息工程学院,西安 710048
    基金项目: 

    国家自然科学基金(批准号:60804040)资助的课题.

摘要: 提出了基于最小二乘支持向量机(LS-SVM)的分数阶混沌系统控制方法.基于分数阶线性系统稳定理论,通过线性分离的方法将系统分解为稳定的线性部分和相应的非线性部分,再利用支持向量机良好的非线性函数逼近和泛化能力设计了主动控制器,对非线性部分进行补偿,从而将分数阶混沌系统控制到平衡点.分别以分数阶Liu系统和分数阶Chen系统为例进行了仿真研究,表明该方法是有效和可行的.

English Abstract

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