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非匹配不确定交叉严反馈超混沌系统神经网络反演同步

李海燕 胡云安 任建存 朱敏 刘亮

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非匹配不确定交叉严反馈超混沌系统神经网络反演同步

李海燕, 胡云安, 任建存, 朱敏, 刘亮

Neural network-based backstepping design for the synchronization of cross-strict feedback hyperchaotic systems with unmatched uncertainties

Li Hai-Yan, Hu Yun-An, Ren Jian-Cun, Zhu Min, Liu Liang
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  • 针对一类具有非匹配不确定性的交叉严反馈超混沌系统,提出一种基于多层前向神经网络的反演自适应同步设计方法.利用神经网络估计系统中的不确定性,运用滑模控制和交叉自适应反演控制处理系统中的非匹配不确定性及神经网络的逼近误差, 当虚拟控制项系数不过零时可保证系统的同步误差趋向于零,过零时可保证同步误差有界. 数值仿真证明了提出的控制方案的有效性.
    For a class of cross-strict feedback hyperchaotic systems with unmatched uncertainties, a multilayer neural network (MNN) based adaptive backstepping design method is proposed. An MNN is introduced to estimate the uncertainties in systems. Sliding mode and adaptive backstepping control are used to deal with the unmatched uncertainties and the MNN approximation errors. If the virtual control coefficients do not pass through zeros, the proposed method guarantees that the synchronization errors of the systems approach zeros. If the virtual control coefficients pass through zeros, the proposed method guarantees that the synchronization errors of the systems are bounded. Numerical simulations are given to demonstrate the efficiency of the proposed control scheme.
    • 基金项目: 国家自然科学基金(批准号: 60674090)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 60674090).
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    Chen F X, Wang W, Chen L, Zhang W D 2007 Phys. Scr. 75 285

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    Haeri M, Emadzadeh A A 2007 Chaos, Solitons and Fractals 31 119

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    Yan J J, Hung M L, Chiang T Y, Yang Y S 2006 Phys. Lett. A 356 220

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    Roopaei M, Sahraei B R, Lin T C 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 4158

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    Yau H T 2008 Mech. Syst. Signal Process 22 408

    [24]

    Wang H, Han Z Z, Xie Q Y, Zhang W 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2728

    [25]

    Xiang W, Huangpu Y G 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3241

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    Guo H J, Lin S F, Liu J H 2006 Phys. Lett. A 351 257

    [27]

    Lu Z, Shieh L S, Chen G R, Coleman N P 2006 Inf. Sci. 176 2337

    [28]

    Zhang N N , Zhang D J, Feng Y 2007 Control and Decis. 22 1143 (in Chinese) [张袅娜, 张德江, 冯勇 2007 控制与决策 22 1143]

    [29]

    Guo H J, Liu D, Zhao G Z 2011 Acta Phys. Sin. 60 010510 (in Chinese) [郭会军, 刘丁, 赵光宙 2011 物理学报 60 010510]

    [30]

    Krstic M, Kanellakopoulos I, Kokotovic P 1995 Nonlinear and Adaptive Control Design (New York: Wiley) p1

    [31]

    Li G H, Zhou S P, Yang K 2006 Phys. Lett. A 355 326

    [32]

    Li H Y, Hu Y A 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3904

    [33]

    Li Y, Tang W K S, Chen G R 2005 Int. J. Bifur. Chaos 15 3367

    [34]

    Wu X Y, Guan Z H, Wu Z P 2008 Nonlinear Anal. 68 1346

    [35]

    Zhang T, Ge S S, Hang C C 1999 Automatica 35 1809

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    Sun Y J, Lien C H, Hsieh J G 1998 IEEE Trans. Autom. Control. 43 674

  • [1]

    Wu T, Chen M S 2002 Physica D 164 53

    [2]

    Harb A, Abedl-Jabbar N 2003 Chaos, Solitons and Fractals 18 1055

    [3]

    Chen G 1999 Controlling Chaos and Bifurcations in Engineering Systems (1st Ed.) (Boca Raton: CRC Press) p10

    [4]

    Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821

    [5]

    Zhu C X 2009 Appl. Math. Comput. 215 557

    [6]

    Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1

    [7]

    Yan Z 2005 Appl. Math. Comput. 168 1239

    [8]

    Wang F, Liu C 2006 Phys. Lett. A 360 274

    [9]

    Wu X Y, Zhang H M 2009 Chaos, Solitons and Fractals 39 2268

    [10]

    Jia Q 2007 Phys. Lett. A 362 424

    [11]

    Zhou X B, Wu Y, Li Y, Xue H Q 2009 Chaos, Solitons and Fractals 39 2477

    [12]

    Wang J, Gao J F, Ma X K 2007 Phys. Lett. A 369 452

    [13]

    Zhang H, Ma X K, Li M, Zou J L 2005 Chaos, Solitons and Fractals 26 353

    [14]

    Yu Y G, Zhang S C 2004 Chaos, Solitons and Fractals 21 643

    [15]

    Tan X H, Zhang J Y, Yang Y R 2003 Chaos, Solitons and Fractals 16 37

    [16]

    Wang C, Ge S S 2001 Int. J. Bifur. Chaos 11 1743

    [17]

    Bowong S, Kakmeni F M M 2004 Chaos, Solitons and Fractals 21 999

    [18]

    Kittel A, Parisi J, Pyragas K 1995 Phys. Lett. A 198 433

    [19]

    Chen F X, Wang W, Chen L, Zhang W D 2007 Phys. Scr. 75 285

    [20]

    Haeri M, Emadzadeh A A 2007 Chaos, Solitons and Fractals 31 119

    [21]

    Yan J J, Hung M L, Chiang T Y, Yang Y S 2006 Phys. Lett. A 356 220

    [22]

    Roopaei M, Sahraei B R, Lin T C 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 4158

    [23]

    Yau H T 2008 Mech. Syst. Signal Process 22 408

    [24]

    Wang H, Han Z Z, Xie Q Y, Zhang W 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2728

    [25]

    Xiang W, Huangpu Y G 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3241

    [26]

    Guo H J, Lin S F, Liu J H 2006 Phys. Lett. A 351 257

    [27]

    Lu Z, Shieh L S, Chen G R, Coleman N P 2006 Inf. Sci. 176 2337

    [28]

    Zhang N N , Zhang D J, Feng Y 2007 Control and Decis. 22 1143 (in Chinese) [张袅娜, 张德江, 冯勇 2007 控制与决策 22 1143]

    [29]

    Guo H J, Liu D, Zhao G Z 2011 Acta Phys. Sin. 60 010510 (in Chinese) [郭会军, 刘丁, 赵光宙 2011 物理学报 60 010510]

    [30]

    Krstic M, Kanellakopoulos I, Kokotovic P 1995 Nonlinear and Adaptive Control Design (New York: Wiley) p1

    [31]

    Li G H, Zhou S P, Yang K 2006 Phys. Lett. A 355 326

    [32]

    Li H Y, Hu Y A 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3904

    [33]

    Li Y, Tang W K S, Chen G R 2005 Int. J. Bifur. Chaos 15 3367

    [34]

    Wu X Y, Guan Z H, Wu Z P 2008 Nonlinear Anal. 68 1346

    [35]

    Zhang T, Ge S S, Hang C C 1999 Automatica 35 1809

    [36]

    Sun Y J, Lien C H, Hsieh J G 1998 IEEE Trans. Autom. Control. 43 674

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出版历程
  • 收稿日期:  2011-10-31
  • 修回日期:  2011-12-13
  • 刊出日期:  2012-07-05

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