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Time-delayed generalized projective synchronization of piecewise chaotic system with unknown parameters

Hu Shou-Song Tao Hong-Feng

Time-delayed generalized projective synchronization of piecewise chaotic system with unknown parameters

Hu Shou-Song, Tao Hong-Feng
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  • The time-delayed generalized projective synchronization problem for a class of piecewise modified Lorenz-Stenflo chaotic system with unknown parameters is discussed. The adaptive nonlinear feedback controller and the parameter update rules are designed based on the Lyapunov stability theory, and the feedback gain can be adjusted adaptively according to the error values and the states. The method can make all full states asymptotically generalized projected synchronization and identify the real-time drive system and the time-delayed response system’s unknown parameters. Results of simulation verified the realistic feasibility and effectiveness of the proposed method to the time-delayed generalized projective synchronization of the piecewise chaotic system.
    • Funds:
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    Lü J H, Zhou T S, Chen G R, Yang X S 2002 Chaos 12 344

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    Elabbasy E M, Agiza H N, EI-Dessoky M M 2004 Int. J. Bifurcation and Chaos 14 3969

    [3]

    Shan L, Liu Z, Li J, Wang Z Q 2009 Inform. Contr. 38 637(in Chinese) [单 梁、刘 中、李 军、王执铨 2009 信息与控制 38 637]

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    Shan L, Li J, Wang Z Q 2006 Acta Phys. Sin. 55 3950 (in Chinese)[单 梁、李 军、王执铨 2006物理学报 55 3950]

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    Zheng Z H, Lü J H, Chen G R, Zhou T S, Zhang S C 2004 Chaos, Solitons and Fractals 20 277

    [6]

    Wang M J, Wang X Y 2009 Acta Phys. Sin. 58 1467 (in Chinese)[王明军、王兴元 2009物理学报 58 1467]

    [7]

    Li W, Hao J H, Qi B 2008 Acta Phys. Sin. 57 1398 (in Chinese)[李 伟、 郝建红、 祁 兵2008物理学报 57 1398]

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    Chen S H, Kong C C 2009 Chin. Phys. B 18 91

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    Yang D S, Zhang H G, Zhao Y, Song C H, Wang Y C 2010 Acta Phys. Sin. 59 1562 (in Chinese)[杨东升、 张化光、 赵 琰、 宋崇辉、 王迎春 2010物理学报 59 1562]

    [10]

    Zhang R X, Tian G, Su P, Yang S P 2008 Acta Phys. Sin. 57 2073 (in Chinese)[张若洵、 田 钢、 粟 苹、 杨世平 2008物理学报 57 2073]

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    Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969

    [12]

    Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3751

    [13]

    Zhang H G, Ma D Z, Wang Z S, Feng J 2010 Acta Phys. Sin. 59 147 (in Chinese)[张化光、 马大中、 王占山、 冯 健 2010物理学报 59 147]

    [14]

    Luo Q, Gao Y, Qi Y N, Gao Y, Wu T, Xu H, Li L X, Yang Y X 2009 Acta Phys. Sin. 58 6809 (in Chinese)[罗 群、 高 雅、 齐雅楠、 高 雅、 吴 桐、 许 欢、 李丽香、 杨义先 2009物理学报 58 6809]

    [15]

    Li G H 2006 Chaos, Solitons and Fractals 30 77

    [16]

    Yan J P, Li C P 2005 Chaos, Solitons and Fractals 26 1119

    [17]

    Li C P, Yan J P 2006 Chaos, Solitons and Fractals 30 140

    [18]

    Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 1441 (in Chinese)[胡建兵、 韩 炎 赵灵冬 2009物理学报 58 1441]

    [19]

    Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese)[蔡 娜、 井元伟、 张嗣瀛 2009物理学报 58 802]

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    Tommy E 2005 Ph.D. Dissertation(Stockholm: KTH)

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    Yang S P, Zhang R X 2009 Chin. Phys.  B 18 3295

  • [1]

    Lü J H, Zhou T S, Chen G R, Yang X S 2002 Chaos 12 344

    [2]

    Elabbasy E M, Agiza H N, EI-Dessoky M M 2004 Int. J. Bifurcation and Chaos 14 3969

    [3]

    Shan L, Liu Z, Li J, Wang Z Q 2009 Inform. Contr. 38 637(in Chinese) [单 梁、刘 中、李 军、王执铨 2009 信息与控制 38 637]

    [4]

    Shan L, Li J, Wang Z Q 2006 Acta Phys. Sin. 55 3950 (in Chinese)[单 梁、李 军、王执铨 2006物理学报 55 3950]

    [5]

    Zheng Z H, Lü J H, Chen G R, Zhou T S, Zhang S C 2004 Chaos, Solitons and Fractals 20 277

    [6]

    Wang M J, Wang X Y 2009 Acta Phys. Sin. 58 1467 (in Chinese)[王明军、王兴元 2009物理学报 58 1467]

    [7]

    Li W, Hao J H, Qi B 2008 Acta Phys. Sin. 57 1398 (in Chinese)[李 伟、 郝建红、 祁 兵2008物理学报 57 1398]

    [8]

    Chen S H, Kong C C 2009 Chin. Phys. B 18 91

    [9]

    Yang D S, Zhang H G, Zhao Y, Song C H, Wang Y C 2010 Acta Phys. Sin. 59 1562 (in Chinese)[杨东升、 张化光、 赵 琰、 宋崇辉、 王迎春 2010物理学报 59 1562]

    [10]

    Zhang R X, Tian G, Su P, Yang S P 2008 Acta Phys. Sin. 57 2073 (in Chinese)[张若洵、 田 钢、 粟 苹、 杨世平 2008物理学报 57 2073]

    [11]

    Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969

    [12]

    Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3751

    [13]

    Zhang H G, Ma D Z, Wang Z S, Feng J 2010 Acta Phys. Sin. 59 147 (in Chinese)[张化光、 马大中、 王占山、 冯 健 2010物理学报 59 147]

    [14]

    Luo Q, Gao Y, Qi Y N, Gao Y, Wu T, Xu H, Li L X, Yang Y X 2009 Acta Phys. Sin. 58 6809 (in Chinese)[罗 群、 高 雅、 齐雅楠、 高 雅、 吴 桐、 许 欢、 李丽香、 杨义先 2009物理学报 58 6809]

    [15]

    Li G H 2006 Chaos, Solitons and Fractals 30 77

    [16]

    Yan J P, Li C P 2005 Chaos, Solitons and Fractals 26 1119

    [17]

    Li C P, Yan J P 2006 Chaos, Solitons and Fractals 30 140

    [18]

    Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 1441 (in Chinese)[胡建兵、 韩 炎 赵灵冬 2009物理学报 58 1441]

    [19]

    Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese)[蔡 娜、 井元伟、 张嗣瀛 2009物理学报 58 802]

    [20]

    Tommy E 2005 Ph.D. Dissertation(Stockholm: KTH)

    [21]

    Yang S P, Zhang R X 2009 Chin. Phys.  B 18 3295

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  • Received Date:  25 January 2010
  • Accepted Date:  11 May 2010
  • Published Online:  15 January 2011

Time-delayed generalized projective synchronization of piecewise chaotic system with unknown parameters

  • 1. (1)College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; (2)School of Communication and Control Engineering, Jiangnan University, Wuxi 214122, China

Abstract: The time-delayed generalized projective synchronization problem for a class of piecewise modified Lorenz-Stenflo chaotic system with unknown parameters is discussed. The adaptive nonlinear feedback controller and the parameter update rules are designed based on the Lyapunov stability theory, and the feedback gain can be adjusted adaptively according to the error values and the states. The method can make all full states asymptotically generalized projected synchronization and identify the real-time drive system and the time-delayed response system’s unknown parameters. Results of simulation verified the realistic feasibility and effectiveness of the proposed method to the time-delayed generalized projective synchronization of the piecewise chaotic system.

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