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基于在线误差修正自适应SVR的非线性不确定分数阶混沌系统滑模控制

薛楷嘉 王从庆

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基于在线误差修正自适应SVR的非线性不确定分数阶混沌系统滑模控制

薛楷嘉, 王从庆

Sliding mode control of fractional order chaotic system based on an online error correction adaptive SVR

Xue Kai-Jia, Wang Cong-Qing
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  • 提出了一种基于在线误差修正自适应SVR的滑模控制方法, 用于解决一类非线性不确定分数阶混沌系统的控制问题. 分别通过对混沌系统非线性函数的离线SVR估计和基于增量学习的状态跟踪误差在线SVR预测, 解决了不确定分数阶混沌系统模型难以预测的问题. 同时根据Lyapunov稳定性理论设计出SVR权值自适应调整律. 本文以分数阶Arneodo 系统为例进行仿真, 仿真结果表明了, 对于带有外界噪声扰动的非线性不确定分数阶混沌系统, 该方法可以在有限时间内将系统稳定至期望状态, 提高对非线性函数的预测精度, 改善控制性能.
    In this paper, a sliding mode control based on an online error correction adaptive SVR is put forward for a class of fractional order chaotic system with nonlinear uncertainty. In order to solve the problem that the uncertainty of the fractional order chaotic system model is difficult to predict, so the nonlinear function of the system is estimated by the offline SVR and the state trace error is forecasted by using incremental learning adaptive online SVR. In addition, the adaptive parameter adjustment law is selected by using the Lyapunov stability theory. Result of simulation of the fractional order Arneodo system shows that the sliding mode control based on the online error correction adaptive SVR can stabilize the nonlinear uncertain fractional order chaotic system with external noise disturbance to an expected state within a limited time. At the same time, both the control performance and the prediction precision of the system's nonlinear function can be improved.
    • 基金项目: 江苏省科技支撑计划(批准号: BE2014712)和机械制造系统工程国家实验室开放基金(批准号: 201002)资助的课题.
    • Funds: Project supported by the JiangSu Scientific Support Program of China (Grant No. BE2014712), and the Foundation of Manufacturing Systems Engineering State Key Laboratory, China (Grant No. 201002)
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    Li T Z, Wang Y, Luo M K 2014 Chin. Phys. B 23 080501

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    Chen D Y, Liu Y X, Ma X Y, Zhang R F 2011 Chin. Phys. B 20 120506

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    Zhou P, Cheng Y M, Kuang F 2010 Chin. Phys. B 19 090503

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    Huang L L, Xin F, Wang L Y 2011 Acta Phys. Sin. 60 010505 (in Chinese) [黄丽莲, 辛方, 王霖郁 2011 物理学报 60 010505]

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    Chen X R, Liu C X, Wang F Q 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣, 刘崇新, 王发强 2008 物理学报 57 1416]

    [10]

    Zhang B T, Pi Y G 2012 Control and Decision 27 1776 (in Chinese) [张碧陶, 皮佑国 2012 控制与决策 27 1776]

    [11]

    Chen D Y, Zhang R F, Sprott J C, Ma X Y 2012 Nonlinear Dynamics 70 1549

    [12]

    Wang B Q, Lin X L 2009 Computer Engineering and Design 13 3219 (in Chinese) [王勃群, 蔺小林 2009 计算机工程与设计 13 3219]

    [13]

    Xiao H M, Zhao L, Wang C H 2012 Control Theory and Application 28 1621 (in Chinese) [肖会敏, 赵林, 王春花 2012 控制理论与应用 28 1621]

    [14]

    Tang G Y, Pang H P, Sun H Y 2009 Control Theory and Application 8 850 (in Chinese) [唐功友, 逄海萍, 孙慧影 2009 控制理论与应用 8 850]

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    Xiao H R, Li Y B, Zhou F Y, Han Y Z 2011 Electrical Power System and Computers 99 503

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    Wang H, Pi D Y, Sun Y X 2007 Neurocomputing 70 952

  • [1]

    Yan X M, Lin D 2010 Acta Phys. Sin. 59 3043 (in Chinese) [阎晓妹, 刘丁 2010 物理学报 59 3043]

    [2]

    Li T Z, Wang Y, Luo M K 2014 Chin. Phys. B 23 080501

    [3]

    Chen D Y, Liu Y X, Ma X Y, Zhang R F 2011 Chin. Phys. B 20 120506

    [4]

    Zhou P, Cheng Y M, Kuang F 2010 Chin. Phys. B 19 090503

    [5]

    Lin T C, Kuo C H, Balas V E. 2011 International Journal of Computers Communications & Control, September 3, 418-427

    [6]

    Zhao J, Chen J J 2009 Control and Decision 24 1559 (in Chinese) [赵俊, 陈建军 2009 控制与决策 24 1559]

    [7]

    Zhang R X, Yang S P 2011 Chin. Phys. B 20 110506

    [8]

    Huang L L, Xin F, Wang L Y 2011 Acta Phys. Sin. 60 010505 (in Chinese) [黄丽莲, 辛方, 王霖郁 2011 物理学报 60 010505]

    [9]

    Chen X R, Liu C X, Wang F Q 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣, 刘崇新, 王发强 2008 物理学报 57 1416]

    [10]

    Zhang B T, Pi Y G 2012 Control and Decision 27 1776 (in Chinese) [张碧陶, 皮佑国 2012 控制与决策 27 1776]

    [11]

    Chen D Y, Zhang R F, Sprott J C, Ma X Y 2012 Nonlinear Dynamics 70 1549

    [12]

    Wang B Q, Lin X L 2009 Computer Engineering and Design 13 3219 (in Chinese) [王勃群, 蔺小林 2009 计算机工程与设计 13 3219]

    [13]

    Xiao H M, Zhao L, Wang C H 2012 Control Theory and Application 28 1621 (in Chinese) [肖会敏, 赵林, 王春花 2012 控制理论与应用 28 1621]

    [14]

    Tang G Y, Pang H P, Sun H Y 2009 Control Theory and Application 8 850 (in Chinese) [唐功友, 逄海萍, 孙慧影 2009 控制理论与应用 8 850]

    [15]

    Xiao H R, Li Y B, Zhou F Y, Han Y Z 2011 Electrical Power System and Computers 99 503

    [16]

    Wang H, Pi D Y, Sun Y X 2007 Neurocomputing 70 952

计量
  • 文章访问数:  5451
  • PDF下载量:  347
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-09-23
  • 修回日期:  2014-10-30
  • 刊出日期:  2015-04-05

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