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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2020, Vol. 37 ›› Issue (2): 146-154.doi: 10.3969/j.issn.1005-3085.2020.02.002

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分数阶具有不确定项和外扰的超混沌金融系统的滑模同步

毛北行   

  1. 郑州航空工业管理学院数学学院，郑州  450015
  • 收稿日期:2018-02-05 接受日期:2019-09-25 出版日期:2020-04-15 发布日期:2020-06-15
  • 基金资助:
    国家自然科学基金(11801528)；河南省高等学校重点基础专项(20ZX003).

Sliding Mode Synchronization of Fractional-order Hyperchaotic Financial Systems with Uncertainty and Outer Disturbance

MAO Bei-xing   

  1. College of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450015
  • Received:2018-02-05 Accepted:2019-09-25 Online:2020-04-15 Published:2020-06-15
  • Supported by:
    The National Natural Science Foundation of China (11801528); the Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions (20ZX003).

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摘要： 本文利用滑模控制与比例积分滑模控制技巧研究了分数阶具有不确定项和外扰的一类超混沌金融系统的同步问题，运用分数阶微积分设计出滑模函数，通过设计适应规则构造出适应控制器，得到了分数阶不确定超混沌金融系统取得滑模同步和积分滑模同步的两个充分性条件．Matlab 数值仿真验证了理论结果．文中滑模函数的设计、控制器的构造及适应规则的选取对研究整数阶超混沌金融系统的滑模同步具有可移植性，所使用的方法为研究分数阶混沌系统提供了思路，同时分数阶系统的相关结果可以移植到整数阶系统的同步问题．

关键词: 不确定, 超混沌, 积分滑模, 外扰

Abstract: In this paper, the synchronization problem of hyperchaotic fractional-order financial systems with uncertainty and outer disturbances are studied based on the sliding mode control and integral sliding mode control techniques. Two sufficient conditions are established to ensure the fractional-order uncertain hyperchaotic financial systems acquiring sliding mode and integral sliding mode synchronization by designing sliding mode functions and controllers through founding adaptive rules using fractional-order integral and calculus. The conclusions are verified by Matlab numerical simulations. The sliding mode functions, controllers and adaptive rules which are designed in the paper can be planted for studying sliding mode synchronization of integer-order chaotic systems. The approaches used in the paper supply the techniques to study the fractional-order systems and can be extended to the integer-order systems synchronization problems.

Key words: uncertain, hyperchaotic, integral sliding mode, outer disturbance

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