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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 ›› 2025, Vol. 42 ›› Issue (5): 860-874.doi: 10.3969/j.issn.1005-3085.2025.05.005cstr: 32411.14.cjem.CN61-1269/O1.2025.05.005

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分数阶时滞多智能体系统的二分一致性

杨  冉1,2,3,   刘  松1,4,  李晓艳1,4   

  1. 1. 安徽大学数学科学学院，合肥 230601

    2. 安徽建筑大学数理学院，合肥 230601

    3. 安徽建筑大学运筹学与数据科学实验室，合肥 230601

    4. 安徽大学理论数学中心，合肥 230601

  • 收稿日期:2023-01-08 接受日期:2024-09-19 出版日期:2025-10-15 发布日期:2015-12-15
  • 通讯作者: 刘松 E-mail: liusong@ahu.edu.cn
  • 基金资助:
    国家自然科学基金 (12401186; 61803139)；安徽省自然科学基金 (2008085QA19)；安徽省教育厅高等学校自然科学研究项目 (2024AH050080; KJ2019A0004; KJ2018A0470)；安徽省高校优秀青年人才项目 (gxyqZD2020002).

Bipartite Consensus of Fractional Delayed Multi-agent Systems

YANG Ran1,2,3,  LIU Song1,4,  LI Xiaoyan1,4   

  1. 1. School of Mathematical Sciences, Anhui University, Hefei 230601
    2. School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601
    3. Operations Research and Data Science Laboratory, Anhui Jianzhu University, Hefei 230601
    4. The Center for Pure Mathematics, Anhui University, Hefei 230601
  • Received:2023-01-08 Accepted:2024-09-19 Online:2025-10-15 Published:2015-12-15
  • Contact: S. Liu. E-mail address: liusong@ahu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (12401186; 61803139)；the Natural Science Foundation of Anhui Province (2008085QA19); the Natural Science Research Project of Higher Education Institutions of Anhui Provincial Department of Education (2024AH050080; KJ2019A0004; KJ2018A0470); the Outstanding Young Talents Program in Universities of Anhui Province (gxyqZD2020002).

摘要：

主要探讨分数阶时滞多智能体系统在固定和切换拓扑下的二分一致性问题。首先针对固定拓扑，通过设计时滞控制协议，并借助分数阶拉兹密辛理论以及符号图论提出了系统实现二分一致性的几个充分条件。其次针对切换拓扑，利用共同Lyapunov函数方法进一步实现该系统的二分一致性。上述方法有效地解决了由时滞、分数阶导数和切换导致的困难。最后，两个简单的数值例子将验证结论的可行性。

关键词: 二分一致性, 分数阶多智能体系统, 符号有向网络, 时滞, 切换网络

Abstract:

The bipartite consensus of fractional multi-agent systems with delay under fixed and switching topologies is addressed in the article. First, for a fixed topology, a delayed control protocol is developed and several feasible conditions of bipartite consensus are proposed with the help of fractional-order Razumikhin theory and signed graph theory. Secondly, regarding the switching topologies, the bipartite consensus is further investigated by the aid of common Lyapunov function method. The proposed way can commendably surmount the trouble arising from time delay, fractional-order derivative and switchings. Ultimately, the feasibility of theoretical conclusions is verified though two simple examples.

Key words: bipartite consensus, fractional-order multi-agent system, signed directed network, time delay, switching network

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