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山东大学学报(工学版) ›› 2017, Vol. 47 ›› Issue (4): 31-36.doi: 10.6040/j.issn.1672-3961.0.2016.327

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分数阶Victor-Carmen混沌系统的自适应滑模控制

毛北行,程春蕊   

  1. 郑州航空工业管理学院理学院, 河南 郑州 450015
  • 收稿日期:2016-10-18 出版日期:2017-08-20 发布日期:2016-10-18
  • 作者简介:毛北行(1976— ),男,河南洛阳人,副教授,硕士,主要研究方向为复杂网络与混沌同步.E-mail:bxmao329@163.com
  • 基金资助:
    国家自然科学青年基金资助项目(NSFC11501525);河南省科技厅软科学资助项目(142400411192);河南省高等学校青年骨干教师资助计划项目(2013GGJS-142);河南省高等学校重点科研资助项目(15B110011)

Self-adaptive sliding mode control of fractional-order Victor-Carmen chaotic systems

MAO Beixing, CHENG Chunrui   

  1. College of Science, Zhengzhou University of Aeronautics, Zhengzhou 450015, Henan, China
  • Received:2016-10-18 Online:2017-08-20 Published:2016-10-18

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摘要： 根据分数阶微积分的相关理论利用自适应滑模控制方法研究分数阶Victor-Carmen混沌系统的滑模同步控制问题,设计分数阶滑模函数并给出控制器的构造,利用Lyapunov稳定性理论给出严格的数学证明,得到系统取得滑模同步的两个充分性条件。研究结果表明:选取适当的控制律以及滑模面下,分数阶Victor-Carmen系统取得混沌同步。数值算例表明该方法有效。

关键词: Victor-Carmen系统, 分数阶, 混沌同步, 滑模

Abstract: The problem of sliding mode synchronization of fractional-order Victor-Carmen systems was studied using self-adaptive sliding mode control approach based on fractional-order calculus theory. The fractional-order slding mode function was designed, the controllers and the strict proof in mathematics using Lyapunov stability theory were given. Two sufficient conditions were arrived for the fractional order systems getting sliding model synchronization. The research conclusion illustrated that fractional-order multi-scroll systems was sliding mode chaos synchronization under proper controllers and sliding mode surface.The numerical simulations demonsrrated the effectiveness of the proposed method.

Key words: fractional-order, Victor-Carmen systems, chaos synchronization, sliding mode

中图分类号: 

  • O482.4
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