电子学报 ›› 2021, Vol. 49 ›› Issue (4): 775-780.DOI: 10.12263/DZXB.20200316

• 学术论文 • 上一篇    下一篇

不确定分数阶高维混沌系统的自适应滑模同步

毛北行, 王东晓   

  1. 郑州航空工业管理学院数学学院, 河南郑州 450015
  • 收稿日期:2020-03-30 修回日期:2020-10-10 出版日期:2021-04-25 发布日期:2021-04-25
  • 作者简介:毛北行 男,教授,硕导,生于1976年,河南孟津人,电子学会会员,研究领域:分数阶混沌系统滑模同步.E-mail:bxmao329@163.com;王东晓 男,副教授,硕士,生于1974年,河北邢台人,研究领域:混沌同步.E-mail:wdxzzia@126.com
  • 基金资助:
    国家自然科学基金(No.41906003);航空科学基金(No.2017ZD55014)

Self-Adaptive Sliding Mode Synchronization of Uncertain Fractional-Order High-Dimension Chaotic Systems

MAO Bei-xing, WANG Dong-xiao   

  1. School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, Henan 450015, China
  • Received:2020-03-30 Revised:2020-10-10 Online:2021-04-25 Published:2021-04-25

摘要: 混沌及其同步已经成为研究的热点,随着分数阶混沌系统建模的需要,分数阶低阶混沌系统的同步控制已经取得了很多结果,国内外针对分数阶高维混沌系统的同步控制方面的研究还十分罕见,本文考虑了不确定因素和外部扰动的影响,利用自适应滑模方法研究高维不确定分数阶混沌系统的同步,基于同步控制理论给出了滑模函数的设计和控制器的构造,获得分数阶高维不确定混沌系统的自适应滑模同步的充分条件.研究结论说明:设计恰当的滑模函数、控制器和适应规则条件下不确定分数阶高维混沌系统取得自适应滑模同步,并把分数阶的相关结论平推到了整数阶,用仿真例子对分数阶高维混沌系统取得滑模同步充分条件的正确性进行了验证.

关键词: 混沌, 分数阶, 滑模, 自适应, 不确定, 控制

Abstract: Chaos and its synchronization has become a hot topic.With the need of fractional-order chaotic system modeling,many results have been achieved in the synchronization control of fractional low-order chaotic systems.Studies on the synchronization control of fractional high-dimensional chaotic systems at home and abroad are still very rare.In this paper,the influence of uncertainties and external disturbances is considered.The self-adaptive sliding mode synchronization of high-dimension fractional-order chaotic systems is studied based on self-adaptive sliding mode methods.The sliding mode functions are funded and controllers are designed based on synchronization control theory.The sufficient conditions are obtained for high-dimension fractional-order uncertain chaotic systems getting self-adaptive sliding mode synchronization.The conclusion demonstrate that high-dimension fractional-order uncertain chaotic systems can get self-adaptive sliding mode synchronization under appropriate sliding mode functions,controllers and adaptive rules.And we extend the conclusions of fractional-order high-dimension uncertain chaotic system to integer-order.The sufficient conditions for fractional-order high-dimension chaotic systems getting sliding mode synchronization are verified to be correct using numerical simulation examples.

Key words: chaotic, fractional-order, sliding mode, self-adaptive, uncertain, control

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