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本文提出一种PIα 控制器设计方法, 实现了分数阶超混沌Chen系统的混沌同步.首先针对分数阶超混沌Chen系统设计了PIα 控制器, 然后利用改进的双参数Mittag-Leffler 函数估计定理和扩展的Gronwall引理证明了系统的稳定性, 并指出了使分数阶超混沌Chen系统同步的控制器参数需满足的条件.仿真结果证实了所设计方法的有效性.
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关键词:
- 分数阶超混沌Chen系统 /
- 混沌同步 /
- PIα 控制
In this paper, a kind of PIα controller is designed for the synchronization of fractional order hyperchaotic Chen system. The controller is designed according to the fractional order hyperchaotic Chen system. The stability of the system is proved by the improved double parameter Mittag-Leffler function estimate theorem and the extended Gronwall lemma. Furthermore, the condition of controller parameters is pointed out which makes the fractional order hyperchaotic Chen system synchronous. Numerical simulations are presented to verify the effectiveness of the method.[1] Wang J A, Liu H P 2010 Acta Phys. Sin. 59 2265 (in Chinese) [王健安, 刘贺平 2010 59 2265]
[2] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁, 黄娟娟 2006 55 3997]
[3] Yuan F G 2012 Commun. Nonlinear Sci. Numer. Simulat 17 2602
[4] Li D, Deng L M, Du Y X, Yang Y Y 2012 Acta Phys. Sin. 61 050502 (in Chinese) [李东, 邓良明, 杜永霞, 杨媛媛 2012 61 050502]
[5] Podlubny I 1999 IEEE Transactions on Automatic Control 44 208
[6] Batlle V F, Perez R R, Garcia F J, Rodriguez L S 2009 Journal of Process Control 19 506
[7] Tang Y Q, Cui M Y, Hua C C, Li L X, Yang Y X 2012 Expert Systems with Applications 39 6887
[8] Zhao H M, Nie B, Li W, Deng W 2012 Journal of Convergence Information Technology 7 50
[9] Hammamci S E 2008 Nonlinear Dynamic 51 329
[10] Xue D Y, Zhao C N 2007 Control Theory and Appl. 24 771 (in Chinese) [薛定宇, 赵春娜 2007控制理论与应用 24 771]
[11] Sun N, Zhang H G, Wang Z L 2010 Journal of Zhejiang University 44 1288 (in Chinese) [孙宁, 张化光, 王智良 2010 浙江大学学报 44 1288]
[12] Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙宁, 张化光, 王智良 2011 60 050511]
[13] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵, 杨世平, 刘永利 2010 59 1549]
[14] Wang Z L, Zhang H G, Li Y F, Sun N 2010IEEE Chinese Control and Decision Conference Xuzhou, China, May 26-28, 2009 p3557
[15] Park J H 2005 Chaos, Solitons and Fractals 26 959
[16] Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) p34
[17] Bellman R 1943 Duke Math. J. 10 643
[18] Liang J W 2006 Jouranl of China University of Petroleum30 154 (in Chinese) [梁景伟 2006 中国石油大学学报 30 154]
[19] Wang Y M 2005 Matrix Analysis (Beijing: China Machine Press) p82 (in Chinese) [王永茂 2005 矩阵分析(北京:机械工业出版社)第82页]
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[1] Wang J A, Liu H P 2010 Acta Phys. Sin. 59 2265 (in Chinese) [王健安, 刘贺平 2010 59 2265]
[2] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁, 黄娟娟 2006 55 3997]
[3] Yuan F G 2012 Commun. Nonlinear Sci. Numer. Simulat 17 2602
[4] Li D, Deng L M, Du Y X, Yang Y Y 2012 Acta Phys. Sin. 61 050502 (in Chinese) [李东, 邓良明, 杜永霞, 杨媛媛 2012 61 050502]
[5] Podlubny I 1999 IEEE Transactions on Automatic Control 44 208
[6] Batlle V F, Perez R R, Garcia F J, Rodriguez L S 2009 Journal of Process Control 19 506
[7] Tang Y Q, Cui M Y, Hua C C, Li L X, Yang Y X 2012 Expert Systems with Applications 39 6887
[8] Zhao H M, Nie B, Li W, Deng W 2012 Journal of Convergence Information Technology 7 50
[9] Hammamci S E 2008 Nonlinear Dynamic 51 329
[10] Xue D Y, Zhao C N 2007 Control Theory and Appl. 24 771 (in Chinese) [薛定宇, 赵春娜 2007控制理论与应用 24 771]
[11] Sun N, Zhang H G, Wang Z L 2010 Journal of Zhejiang University 44 1288 (in Chinese) [孙宁, 张化光, 王智良 2010 浙江大学学报 44 1288]
[12] Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙宁, 张化光, 王智良 2011 60 050511]
[13] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵, 杨世平, 刘永利 2010 59 1549]
[14] Wang Z L, Zhang H G, Li Y F, Sun N 2010IEEE Chinese Control and Decision Conference Xuzhou, China, May 26-28, 2009 p3557
[15] Park J H 2005 Chaos, Solitons and Fractals 26 959
[16] Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) p34
[17] Bellman R 1943 Duke Math. J. 10 643
[18] Liang J W 2006 Jouranl of China University of Petroleum30 154 (in Chinese) [梁景伟 2006 中国石油大学学报 30 154]
[19] Wang Y M 2005 Matrix Analysis (Beijing: China Machine Press) p82 (in Chinese) [王永茂 2005 矩阵分析(北京:机械工业出版社)第82页]
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