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基于Lyapunov方程的分数阶新混沌系统的控制

许喆 刘崇新 杨韬

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基于Lyapunov方程的分数阶新混沌系统的控制

许喆, 刘崇新, 杨韬

Controlling fractional-order new chaotic system based on Lyapunov equation

Xu Zhe, Liu Chong-Xin, Yang Tao
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  • 新混沌系统是一种不同于Lorenz混沌系统、Chen混沌系统以及Liu混沌系统的新的三阶连续自治混沌系统.本文基于波特图的频域近似方法,提出了一种混合型电路单元来近似实现分数阶算子,并设计电路实现了27阶新混沌系统.基于Lyapunov方程的系统稳定性判定理论,设计了相应的控制器,实现了对分数阶新混沌系统的控制.
    A new circuit unit for the analysis and synthesis of the chaotic behaviors in the new fractional-order system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to demonstrate the dynamic behaviors of the fractional-order Liu system with α=09 An effective controller is designed based on a theory of stability identification based on Lyapunov equation. The results between simulation and experiment are in good agreement, thereby proving the existence of chaos in the fractional-order new system and the effectiveness of our proposed control method.
    [1]

    [1]Hartly T T, Lorenzo C F, Qammer H K 1995 IEEE Trans. CAS-I 42 485

    [2]

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

    [3]

    [3]Li C P, Peng G J 2004 Chaos,Solitons and Fractals. 22 443

    [4]

    [4]Li C G, Chen G R 2004 Chaos, Solitions and Fractals 22 549

    [5]

    [5]Deng W H, Li C P 2005 Physica A 353 61

    [6]

    [6]Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922 (in Chinese)[王发强、刘崇新 2006 物理学报 55 3922]

    [7]

    [7]Lu J J, Liu C X 2007 Chin. Phys. 16 1586

    [8]

    [8]Xu Z, Liu C X 2008 Chin.Phys. B 17 4033

    [9]

    [9]Li C G, Chen G R 2004 Physica A 341 55

    [10]

    [10]Liu C X 2006 Far East J. Dynamical System 8 51

    [11]

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

    [12]

    [12]Charef A, Sun H H, Tsao Y Y, Onaral B 1992 IEEE Trans. Auto. Contr. 37 9

    [13]

    [13]Liu C X,Liu T,Liu K,Liu L 2004 Chaos, Solitions and Fractals 22 1031

    [14]

    [14]Ahmad W M, Sprott J C 2003 Chaos, Solitons and Fractals 16 339

    [15]

    [15]Zhao P D, Zhang X D 2008 Acta Phys. Sin. 57 2791 (in Chinese)[赵品栋、张晓丹 2008 物理学报 57 2791]

    [16]

    [16]Matignon D 1996 In: IMACS, IEEE-SMC, Lille, France 963

    [17]

    [17]Hu J B, Han Y, Zhao L D. 2008 Acta Phys. Sin 57 7522 (in chinese)[胡建兵、韩焱、赵灵冬 2008 物理学报 57 7522]

  • [1]

    [1]Hartly T T, Lorenzo C F, Qammer H K 1995 IEEE Trans. CAS-I 42 485

    [2]

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

    [3]

    [3]Li C P, Peng G J 2004 Chaos,Solitons and Fractals. 22 443

    [4]

    [4]Li C G, Chen G R 2004 Chaos, Solitions and Fractals 22 549

    [5]

    [5]Deng W H, Li C P 2005 Physica A 353 61

    [6]

    [6]Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922 (in Chinese)[王发强、刘崇新 2006 物理学报 55 3922]

    [7]

    [7]Lu J J, Liu C X 2007 Chin. Phys. 16 1586

    [8]

    [8]Xu Z, Liu C X 2008 Chin.Phys. B 17 4033

    [9]

    [9]Li C G, Chen G R 2004 Physica A 341 55

    [10]

    [10]Liu C X 2006 Far East J. Dynamical System 8 51

    [11]

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

    [12]

    [12]Charef A, Sun H H, Tsao Y Y, Onaral B 1992 IEEE Trans. Auto. Contr. 37 9

    [13]

    [13]Liu C X,Liu T,Liu K,Liu L 2004 Chaos, Solitions and Fractals 22 1031

    [14]

    [14]Ahmad W M, Sprott J C 2003 Chaos, Solitons and Fractals 16 339

    [15]

    [15]Zhao P D, Zhang X D 2008 Acta Phys. Sin. 57 2791 (in Chinese)[赵品栋、张晓丹 2008 物理学报 57 2791]

    [16]

    [16]Matignon D 1996 In: IMACS, IEEE-SMC, Lille, France 963

    [17]

    [17]Hu J B, Han Y, Zhao L D. 2008 Acta Phys. Sin 57 7522 (in chinese)[胡建兵、韩焱、赵灵冬 2008 物理学报 57 7522]

计量
  • 文章访问数:  8606
  • PDF下载量:  1588
  • 被引次数: 0
出版历程
  • 收稿日期:  2009-04-22
  • 修回日期:  2009-07-04
  • 刊出日期:  2010-03-15

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