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随机扰动下一般混沌系统的H∞同步

涂俐兰 柯超 丁咏梅

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随机扰动下一般混沌系统的H∞同步

涂俐兰, 柯超, 丁咏梅

H∞ synchronization of general chaotic systems with random perturbations

Tu Li-Lan, Ke Chao, Ding Yong-Mei
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  • 本文对随机扰动下的一般混沌系统进行了H∞控制同步研究,其中扰动是布朗运动随机过程.基于随机李雅普诺夫稳定性理论、线性矩阵不等式、It公式以及H∞控制方法,通过设置控制器,从理论上提出了驱动系统和随机扰动下的响应系统的H∞渐近同步的新标准,这些标准形式简单且易于用Matlab实现.最后的数值模拟表明提出的理论结果的正确性和有效性.
    In this paper, the H∞ synchronization of general chaotic systems with random perturbations is investigated, in which perturbation is a random process of Brownian motion. Based on stochastic Lyapunov stability theory, linear matrix inequalities, and It formula and H∞ control method combined with feedback control laws, some new asymptotic synchronization schemes are established which guarantee robust stochastical mean square asymptotical synchronization for drive system and noise-perturbed response system, as well as achieving a prescribed stochastic robust H∞ performance level. These schemes are in a simple form and easy to work with Matlab. Finally, simulations show that the proposed results are correct and effective.
    • 基金项目: 国家自然科学基金 (批准号:60904060),冶金工业过程系统科学湖北省重点实验室开放基金 (批准号:C201010) 资助的课题.
    [1]

    Ott E, Grebogi C, Yorke J A 1990 Phys. Lett. 64 1196

    [2]

    Pecora L M, Carroll T L 1990 Phys.Rec.Let. 64 821

    [3]

    Tu L L, Lu J A 2005 Chin. Phys. 14 1755

    [4]

    Cai G L, Tan Z M, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、谭振梅、周维怀、涂文桃 2007 物理学报 56 6230]

    [5]

    Gong L H 2005 Acta Phys. Sin. 54 3502 (in Chinese) [龚礼华 2005 物理学报 54 3502]

    [6]

    Zhang H B, Yu Y B, Zhang J 2010 Chin. Phys. B 19 080509-1

    [7]

    Chen G R, Lv J H 2003 Dynamics analysis, control and synchronization of Lorenz system family (Beijing: Science Press) p2 (in Chinese) [陈关荣、吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京: 科学出版社) 第2页]

    [8]

    Chen G, Dong X 1998 From chaos to order:Methodologies, Perspectives and Application (Singapore: World Scientifi) p4

    [9]

    Lorenz E N 1963 J. Atmos. Sci. 20 130

    [10]

    Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. On Circuits & Systems-Ⅰ 33 1072

    [11]

    Chen G R, Ueta T 1999 Int. J. of Bifur Chaos 9 1465

    [12]

    Lü J H, Chen G R 2002 Int. J. of Bifur Chaos 12 659

    [13]

    Liu C X, Liu T, Liu L, Liu K 2004 Chaos, Solitons and Fractals 22 1031

    [14]

    Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese) [武相军、王兴元 2006物理学报 55 6261]

    [15]

    Liu Y Z, Jiang C S, Lin C S 2008 Acta Phys. Sin. 57 6808 (in Chinese) [刘扬正、姜长生、林长圣 2008 物理学报 57 6808]

    [16]

    Chen G P, Hao J B 2008 Communications Technology 41 230 (in Chinese)[陈光平、郝加波 2008 通信技术 41 230]

    [17]

    Chen A M, Lu J A, Lv J H 2006 Physics A 364 103

    [18]

    Zames G 1981 IEEE Trans. Automatic Control 26 301

    [19]

    Wei R, Wang X Y 2004 Acta Phys. Sin. 53 3298 (in Chinese) [魏 荣、王行愚 2004 物理学报 53 3298]

    [20]

    Yan J J 2004 Chaos, Solitons and Fractals 21 283

    [21]

    Hou Y Y, Liao T L, Yan J J 2007 Physica A 379 81

    [22]

    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]

    [23]

    Park J H, Ji D H, Won S C, Lee S M 2008 Applied Mathematics and Computation 204 170

    [24]

    Anton S 1992 The H∞ Control Problem (New York: Prentice-Hall) p5

    [25]

    Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System

  • [1]

    Ott E, Grebogi C, Yorke J A 1990 Phys. Lett. 64 1196

    [2]

    Pecora L M, Carroll T L 1990 Phys.Rec.Let. 64 821

    [3]

    Tu L L, Lu J A 2005 Chin. Phys. 14 1755

    [4]

    Cai G L, Tan Z M, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、谭振梅、周维怀、涂文桃 2007 物理学报 56 6230]

    [5]

    Gong L H 2005 Acta Phys. Sin. 54 3502 (in Chinese) [龚礼华 2005 物理学报 54 3502]

    [6]

    Zhang H B, Yu Y B, Zhang J 2010 Chin. Phys. B 19 080509-1

    [7]

    Chen G R, Lv J H 2003 Dynamics analysis, control and synchronization of Lorenz system family (Beijing: Science Press) p2 (in Chinese) [陈关荣、吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京: 科学出版社) 第2页]

    [8]

    Chen G, Dong X 1998 From chaos to order:Methodologies, Perspectives and Application (Singapore: World Scientifi) p4

    [9]

    Lorenz E N 1963 J. Atmos. Sci. 20 130

    [10]

    Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. On Circuits & Systems-Ⅰ 33 1072

    [11]

    Chen G R, Ueta T 1999 Int. J. of Bifur Chaos 9 1465

    [12]

    Lü J H, Chen G R 2002 Int. J. of Bifur Chaos 12 659

    [13]

    Liu C X, Liu T, Liu L, Liu K 2004 Chaos, Solitons and Fractals 22 1031

    [14]

    Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese) [武相军、王兴元 2006物理学报 55 6261]

    [15]

    Liu Y Z, Jiang C S, Lin C S 2008 Acta Phys. Sin. 57 6808 (in Chinese) [刘扬正、姜长生、林长圣 2008 物理学报 57 6808]

    [16]

    Chen G P, Hao J B 2008 Communications Technology 41 230 (in Chinese)[陈光平、郝加波 2008 通信技术 41 230]

    [17]

    Chen A M, Lu J A, Lv J H 2006 Physics A 364 103

    [18]

    Zames G 1981 IEEE Trans. Automatic Control 26 301

    [19]

    Wei R, Wang X Y 2004 Acta Phys. Sin. 53 3298 (in Chinese) [魏 荣、王行愚 2004 物理学报 53 3298]

    [20]

    Yan J J 2004 Chaos, Solitons and Fractals 21 283

    [21]

    Hou Y Y, Liao T L, Yan J J 2007 Physica A 379 81

    [22]

    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]

    [23]

    Park J H, Ji D H, Won S C, Lee S M 2008 Applied Mathematics and Computation 204 170

    [24]

    Anton S 1992 The H∞ Control Problem (New York: Prentice-Hall) p5

    [25]

    Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System

计量
  • 文章访问数:  7083
  • PDF下载量:  693
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-08-09
  • 修回日期:  2010-09-06
  • 刊出日期:  2011-05-15

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