基于滑模趋近律的忆阻混沌系统有限和固定时间同步

赖强; 王君

doi:10.7498/aps.73.20241013

摘要

针对一类具有更复杂动力学行为的忆阻混沌系统, 本文基于新型幂次趋近律设计两种滑模控制协议分别实现了系统的有限时间、固定时间同步. 首先对于有限时间同步问题, 基于Lyapunov稳定性理论和有限时间稳定性理论, 推导了实现全局有限时间同步的充分条件, 得到了与系统初始条件有关的稳定时间上限, 并证明了系统的稳定性. 对于固定时间同步问题, 利用固定时间稳定性理论, 推导得到不随系统初始值变化的收敛时间上确界. 最后, 通过设置两组对照实验, 比较了两种滑模控制律对系统同步状态的影响, 其仿真结果与数值分析相符, 从而验证了本文的有效性和可行性.

关键词:

Abstract

Two innovative sliding mode control laws based on the convergence principle of reaching law are presented in this work. These control laws are used to achieve both finite-time and fixed-time synchronization for a specific class of memristive chaotic system, which are known for their intricate and complex dynamical behaviors. By utilizing these control strategies, we can effectively manage the synchronization process and ensure rapid convergence. Firstly, for the finite-time synchronization issue, a novel power reaching law is derived. Compared with the conventional reaching law, the reaching law presented in this work has a prominent advantage that the chattering of the sliding mode control is reduced to a lesser extent and the speed of reaching the sliding surface is quicker. An upper bound of the stabilization time, which is dependent on the initial conditions of the system, is obtained and the system is proved stable. For the fixed time synchronization problem, a new double power reaching law is put forward to minimize the chattering and accelerate the convergence. Then, by utilizing the fixed time stability theory, the upper bound of the convergence time that remains invariant with the initial value of the system is derived. Finally, in order to verify the effectiveness and feasibility of the theoretical derivation in this paper, two sets of control experiments are set up and the influences of the two control laws on the system synchronization state are compared. The experimental phenomenon strongly proves the accuracy of the proposed theorem.

Keywords:

作者及机构信息

赖强,
王君

华东交通大学电气与自动化工程学院, 南昌　330013

通信作者: 赖强, laiqiang87@126.com

基金项目: 国家自然科学基金(批准号: 62366014)资助的课题.

Authors and contacts

Lai Qiang,
Wang Jun

School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China

Corresponding author: Lai Qiang, laiqiang87@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 62366014).

文章全文

参考文献

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施引文献

图 1 驱动系统(1)的状态变量轨迹

Fig. 1. Trajectory of the state variables of drive system (1).

下载: 全尺寸图片幻灯片

图 2 忆阻混沌系统(1)吸引子相图　(a) x -y平面; (b) x -w平面; (c) x -z平面; (d) y -w平面

Fig. 2. Attractor phase diagrams of the memristor chaotic system (1): (a) x -y plane; (b) x -w plane; (c) x -z plane; (d) y -w plane.

下载: 全尺寸图片幻灯片

图 3 初始状态为$ {x_1}(0) = ( - 1, {\text{ }}2, {\text{ }}3, {\text{ }} - 4) $时有限时间同步误差

Fig. 3. Finite time synchronization error when the initial state is $ {x_1}(0) = ( - 1, {\text{ }}2, {\text{ }}3, {\text{ }} - 4) $.

下载: 全尺寸图片幻灯片

图 4 初始状态为$ {x_2}(0) = ( - 10, {\text{ }}20, {\text{ }}30, {\text{ }} - 40) $时有限时间同步误差

Fig. 4. Finite time synchronization error when the initial state is $ {x_2}(0) = ( - 10, {\text{ }}20, {\text{ }}30, {\text{ }} - 40) $.

下载: 全尺寸图片幻灯片

图 5 初始状态为$ {x_1}(0) = ( - 1, {\text{ }}2, {\text{ }}3, {\text{ }} - 4) $时固定时间同步误差

Fig. 5. Fixed time synchronization error when the initial state is $ {x_1}(0) = ( - 1, {\text{ }}2, {\text{ }}3, {\text{ }} - 4) $.

下载: 全尺寸图片幻灯片

图 6 初始状态为$ {x_2}(0) = ( - 10, {\text{ }}20, {\text{ }}30, {\text{ }} - 40) $时固定时间同步误差

Fig. 6. Fixed time synchronization error when the initial state is $ {x_2}(0) = ( - 10, {\text{ }}20, {\text{ }}30, {\text{ }} - 40) $.

下载: 全尺寸图片幻灯片

[1]	An X L, Liu S Y, Xiong L, Zhang J G, Li X Y 2024 Expert Syst. Appl. 243 122899 Google Scholar
[2]	Lai Q, Yang L, Hu G W, Guan Z H, Iu H H C 2024 IEEE Trans. Cybern. 54 4039 Google Scholar
[3]	Lai Q, Yang L, Chen G R 2024 IEEE Trans. Ind. Electron. 71 7819 Google Scholar
[4]	Ji X Y, Dong Z K, Han Y F, Lai C S, Qi D L 2023 IEEE Trans. Circuits Syst. Video Technol. 33 7928 Google Scholar
[5]	Ji X Y, Dong Z K, Han Y F, Lai C S, Zhou G D, Qi D L 2023 IEEE Trans. Consum. Electr. 69 1005 Google Scholar
[6]	Babanli K M, Kabaoglu R O 2024 Inf. Sci 657 119988 Google Scholar
[7]	王国超, 李星辉, 颜树华, 谭立龙, 管文良 2021 物理学报 70 040601 Google Scholar Wang G C, Li X H, Yan S H, Tan L L, Guan W L 2021 Acta Phys. Sin. 70 040601 Google Scholar
[8]	Zheng H, Zhu W, Li X 2024 Chaos Soliton Fract. 180 114496 Google Scholar
[9]	王栋梁, 史卓, 王井上, 吴洪悦, 张晓辉, 常国庆 2024 物理学报 73 134204 Google Scholar Wang D L, Shi Z, Wang J S, Wu H Y, Zhang X H, Chang G Q 2024 Acta Phys. Sin. 73 134204 Google Scholar
[10]	Lai Q, Chen Z J 2023 Chaos Soliton Fract. 176 114118 Google Scholar
[11]	张骁骏, 袁夏明, 王向阳, 朱纪洪, 李春文 2022 自动化学报 48 712 Google Scholar Zhang X J, Yuan X M, Wang X Y, Zhu J H, Li C W 2022 Acta Autom. Sin. 48 712 Google Scholar
[12]	Mobayen S 2018 ISA T 77 100 Google Scholar
[13]	吴朝俊, 方礼熠, 杨宁宁 2024 物理学报 73 010501 Google Scholar Wu C J, Fang L Y, Yang N N 2024 Acta Phys. Sin. 73 010501 Google Scholar
[14]	Junejo A K, Xu W, Mu C, Ismail M M, Liu Y 2020 IEEE Trans. Power Electron. 35 12110 Google Scholar
[15]	王宇娟, 涂俐兰, 宋帅, 李宽洋 2018 物理学报 67 050504 Google Scholar Wang Y J, Tu L L, Song S, Li K Y, 2018 Acta Phys. Sin. 67 050504 Google Scholar
[16]	Lai Q, Yang L 2023 Chaos Soliton Fract. 174 113807 Google Scholar
[17]	Hao Y, Fang Z, Liu H 2024 Inf. Sci. 666 120423 Google Scholar
[18]	Bhat S P, Bernstein D S 2000 SIAM J. Control Optim. 38 751 Google Scholar
[19]	Dong H L, Cao J D, Liu H 2023 Chaos 33 043113 Google Scholar
[20]	Fu H, Kao Y G 2023 Chaos 33 043136 Google Scholar
[21]	Polyakov A 2011 IEEE Trans. Autom. Control 57 8 Google Scholar
[22]	Ullah S, Khan Q, Zaidi M M, Hua L G 2024 Inf. Sci. 659 120087 Google Scholar
[23]	Zheng C C, Hu C, Yu J, Wen S P 2024 Neural Netw. 169 32 Google Scholar
[24]	Hu X, Wang L, Zhang C K, He Y 2024 IEEE Trans. Fuzzy Syst. 32 2307 Google Scholar
[25]	Wang L, Dong T, Ge M F 2019 Appl. Math. Comput. 347 293 Google Scholar
[26]	Fallaha C J, Saad M, Kanaan H Y, Haddad K A 2010 IEEE Trans. Ind. Electron. 58 600 Google Scholar
[27]	Wang L, Jiang S, Ge M F, Hu C, Hu J H 2021 IEEE Trans. Circuits Syst. I: Regul. Pap. 68 4957 Google Scholar

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基于滑模趋近律的忆阻混沌系统有限和固定时间同步