具有对抗关系和时变拓扑的耦合离散系统有界双向同步

翟世东; 刘佩; 高辉

doi:10.16383/j.aas.c190251

具有对抗关系和时变拓扑的耦合离散系统有界双向同步

doi: 10.16383/j.aas.c190251 cstr: 32138.14.j.aas.c190251

翟世东^{1, 2,},
刘佩^{1, 2,},
高辉^{1, 2,}

1.
重庆邮电大学自动化学院重庆 400065
2.
重庆邮电大学复杂系统与仿生控制重庆市重点实验室重庆 400065

基金项目: 国家自然科学基金(11502039), 重庆市自然科学基金(cstc2019jcyj-msxmX0109), 重庆市教委创新团队项目(CXTDX201601019)资助

详细信息

作者简介:
翟世东：重庆邮电大学自动化学院副教授. 2014年获得华中科技大学博士学位. 主要研究方向为非线性系统控制, 复杂网络动力学与控制. 本文通信作者. E-mail: zhaisd@cqupt.edu.cn

刘佩：重庆邮电大学自动化学院硕士研究生. 2017年获得重庆邮电大学学士学位. 主要研究方向为复杂网络同步. E-mail: LP2017014@163.com

高辉：重庆邮电大学自动化学院硕士研究生. 2018年获得陕西理工大学学士学位. 主要研究方向为复杂网络控制. E-mail: s180331089@stu.cqupt.edu.cn

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出版历程
- 收稿日期: 2019-03-26
- 录用日期: 2019-08-08
- 网络出版日期: 2022-03-01
- 刊出日期: 2022-03-25

Bounded Bipartite Synchronization for Coupled Discrete Systems Under Antagonistic Interactions and Time-varying Topologies

ZHAI Shi-Dong^{1, 2
,},
LIU Pei^{1, 2
,},
GAO Hui^{1, 2
,}

1.
School of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065
2.
Key Laboratory of Complex Systems and Bionics Control of Chongqing Municipality, Chongqing University of Posts and Telecommunications, Chongqing 400065

Funds: Supported by National Natural Science Foundation of China (11502039), Natural Science Foundation of Chongqing of China (cstc2019jcyj-msxmX0109), and Innovation Team Project of Chongqing Education Committee (CXTDX201601019)

More Information

Author Bio:
ZHAI Shi-Dong　Associate professor at the School of Automation, Chongqing University of Posts and Telecommunications. He received his Ph.D. degree from Huazhong University of Science and Technology in 2014. His research interest covers nonlinear system control, and dynamics of complex network and control. Corresponding author of this paper

LIU Pei　Master student at the School of Automation, Chongqing University of Posts and Telecommunications. She received her bachelor degree from Chongqing University of Posts and Telecommunications in 2017. Her main research interest is synchronization of complex network

GAO Hui　Master student at the School of Automation, Chongqing University of Posts and Telecommunications. He received his bachelor degree from Shaanxi University of Technology in 2018. His main research interest is control of complex network

摘要

摘要: 针对含有对抗关系和时变拓扑的耦合离散系统, 本文研究了这类系统有界双向同步问题(Bounded bipartite synchronization, BBS). 考虑了以下两种情形: 1)在某时刻所有个体不能划分为两个敌对阵营; 2)尽管在每一个时刻所有个体都可以被划分为两个敌对阵营, 但每个阵营中的成员随着时间的推移而改变. 对于以上两种情形, 耦合系统不能达到双向同步, 可以在一定条件下达到有界双向同步. 本文得到了使耦合离散系统达到有界双向同步的一些充分条件, 并通过一个数值例子验证了所得结论的有效性.
- 双向同步 /
- 有界双向同步 /
- 符号图 /
- 离散系统
Abstract: For coupled discrete systems with antagonistic interactions and time-varying topologies, this paper studies the bounded bipartite synchronization (BBS) for such coupled systems. This paper considers the following two cases: 1) At some time instants all agents cannot be divided into two hostile camps; 2) Although all agents can be partitioned into two hostile camps, the members of hostile camps change as time goes on. For the above conditions, the coupled systems cannot achieve bipartite synchronization, and can achieve BBS under some conditions. This paper obtains some sufficient conditions such that the coupled discrete system achieves BBS, and one numerical example is provided to illustrate the effectiveness of obtained results.
- Bipartite synchronization /
- bounded bipartite synchronization (BBS) /
- sighed graph /
- discrete systems

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图 1 无向图$G({E^i})$, $i = 1,2$

Fig. 1 The undirected signed graph $G({E^i})$, $i = 1,2$

下载: 全尺寸图片幻灯片

图 2 无向图$G( {\bar {E}^i} )$, $i = 1,2$

Fig. 2 The undirected signed graph $G( {\bar {E}^i} )$, $i = 1,2$

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图 3 四智能体网络在拓扑为图2、切换信号为$ \sigma (k) $时的时间演变过程

Fig. 3 Time evolution of 4-agent network with topologies in Fig.2 and switching signal $ \sigma(k) $

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图 4 四智能体网络在拓扑为图1、切换信号为$ \sigma (k) $时的时间演变过程

Fig. 4 Time evolution of 4-agent network with topologies in Fig.1 and switching signal $ \sigma(k) $

下载: 全尺寸图片幻灯片

图 5 四智能体网络在切换信号$ \sigma(k) $下的范数误差和终值

Fig. 5 Norm error of the 4-agent network with switching signal $ \sigma(k) $

下载: 全尺寸图片幻灯片

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