忆阻器多涡卷混沌系统及其滑模控制同步

量子电子学报 ›› 2020, Vol. 37 ›› Issue (6): 727-736.

忆阻器多涡卷混沌系统及其滑模控制同步

李晓霞1,2∗, 冯志新1,2, 张启宇1,2, 王雪1,2

1 河北工业大学省部共建电工装备可靠性与智能化国家重点实验室, 天津300130; 2 河北工业大学河北省电磁场与电器可靠性重点实验室, 天津300130

收稿日期:2020-02-06 修回日期:2020-04-04 出版日期:2020-11-28 发布日期:2020-11-28
作者简介:李晓霞( 1970 - ), 女, 博士, 副教授, 硕士生导师, 主要从事复杂网络及生物电工方面的研究。E-mail: lixiaoxia@hebut.edu.cn
基金资助:
Supported by Natural Science Foundation of Hebei Province (河北省自然科学基金, E2011202051)

Memristive multi-scroll chaotic system and its synchronization under sliding mode control

LI Xiaoxia 1,2∗, FENG Zhixin 1,2, ZHANG Qiyu 1,2, WANG Xue 1,2

1 State Key Laboratory of Reliability & Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China; 2 Key Laboratory of Electromagnetic Field & Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300130, China

Received:2020-02-06 Revised:2020-04-04 Published:2020-11-28 Online:2020-11-28

摘要/Abstract

摘要： 通过在Yang 系统中添加具有忆阻器性质的项及其他非线性项, 提出了一种忆阻混沌系统。改变该系统的参数及状态变量的初值可得到单涡卷、双涡卷和三涡卷的混沌吸引子。以三涡卷时的系统为例, 分析了其动力学特性, 研究了该系统与加入了干扰信号的Chen 系统的广义同步。应用滑模控制方法设计了同步控制器及参数自适应律, 并基于Lyapunov 稳定性理论得出了实现同步的充分条件, 最后将所提出的同步方法与没有引入滑模控制的方法进行了比较。结果表明两个系统实现了同步, 参数得到了准确的估计, 且该方法比没有引入滑模控制的方法同步速度更快, 抗干扰能力更强。

关键词: 混沌, 广义同步, 滑模控制, 多涡卷混沌系统, 忆阻器

Abstract: A memristive chaotic system is proposed by adding terms with properties of memristor and other nonlinear terms to Yang system. The chaotic attractors with single scroll, double scrolls and triple scrolls can be obtained by changing the parameters and initial values of state variables of the system. The dynamic characteristics of the system are analyzed, and the generalized synchronization between the memristive chaotic system and Chen system with disturbance is investigated by taking a triple-scroll system as an example. The synchronization controller and parameter adaptive law are designed by employing sliding mode control method, and the sufficient conditions for synchronization are obtained by using Lyapunov stability theory. Finally, the proposed synchronization method is compared with the method without sliding mode control. Results show that the two systems are synchronized and the parameters are accurately estimated. The proposed method is faster in synchronization speed than the method without sliding mode control, and has better anti-interference ability as well.

Key words: chaos, generalized synchronization, sliding mode control, multi-scroll chaotic system, memristor

中图分类号:

O415.5

李晓霞, ∗, 冯志新, 张启宇, 王雪, . 忆阻器多涡卷混沌系统及其滑模控制同步[J]. 量子电子学报, 2020, 37(6): 727-736.

LI Xiaoxia , ∗, FENG Zhixin , ZHANG Qiyu , WANG Xue , . Memristive multi-scroll chaotic system and its synchronization under sliding mode control[J]. Chinese Journal of Quantum Electronics, 2020, 37(6): 727-736.

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