切换伪路图下的多智能体能控性

陈英鑫; 纪志坚; 陈英鑫; 纪志坚

doi:10.13306/j.1672-3813.2025.02.017

复杂系统与复杂性科学 >

2025 , Vol. 22 >Issue 2: 135 - 144

DOI: https://doi.org/10.13306/j.1672-3813.2025.02.017

研究论文

切换伪路图下的多智能体能控性

陈英鑫 ,
纪志坚 ,
陈英鑫 ,
纪志坚

展开

1.青岛大学自动化学院,山东青岛 266071;
2.山东省工业控制重点实验室,山东青岛 266071

陈英鑫(1995),男,山东潍坊人,硕士研究生,主要研究方向为多智能体网络系统。

收稿日期: 2023-08-11

修回日期: 2023-10-26

网络出版日期: 2025-06-03

基金资助

国家自然科学基金(62373205,62033007);山东省泰山学者特聘教授人才支持计划(tstp20230624,ts20190930);山东省泰山学者攀登计划。

收起

Controllability of Multi-agent Under Switching Pseudo-paths

CHEN Yingxin ,
JI Zhijian ,
CHEN Yingxin ,
JI Zhijian

Expand

1. School of Automation, Qingdao University, Qingdao 266071, China;
2. Shandong Key Laboratory of Industrial Control Technology, Qingdao 266071, China

Received date: 2023-08-11

Revised date: 2023-10-26

Online published: 2025-06-03

Fold

摘要

设计了一类伪路图并引入切换信号,运用图论和矩阵论研究多智能体系统的能控性。首先,得到多智能体的系统矩阵及其指数函数,获得多智能体系统实现能控性的充要条件;其次,讨论了不同的单领导者选取方式对能控性矩阵的影响;最后,得到系统在给定切换序列下到达能控状态空间任意指定位置的最小切换周期。

关键词： 多智能体系统; 切换系统; 伪路图; 零边节点列表; 能控性

本文引用格式

陈英鑫 , 纪志坚 , 陈英鑫 , 纪志坚 . 切换伪路图下的多智能体能控性[J]. 复杂系统与复杂性科学, 2025 , 22(2) : 135 -144 . DOI: 10.13306/j.1672-3813.2025.02.017

Abstract

This paper introduces a new type of pseudo-path and incorporate switching signals in the study. We apply graph and matrix theories to explore the controllability of multi-agent systems. Firstly, we obtain the system matrix and its exponential function of the multi-agent system, we then derive the necessary and sufficient conditions to achieve controllability. Secondly, we discuss the impact of different ways of selecting a single leader on the controllability matrix. Finally, we determine the minimum switching period for the system to reach any specified position in the controllable state space under a given switching sequence.

Key words： multi-agent system; switched system; pseudo-path; zero-edge node list; controllability

参考文献

[1] TANNER H. On the controllability of nearest neighbor interconnections[C]//Proceedings of the 43^rd IEEE Conference on Decision and Control. Atlantis. Paradise Island, Bahamas, 2004: 24672472.
[2] 武海鹰,王绪安.分布式人工智能与多智能体系统研究[J]. 微机发展, 2004, 14(3): 8082.
WU H Y, WANG X A. Research on multi-agent system and distributed AI[J]. Microcomputer Development, 2004, 14(3): 8082.
[3] 李瑞敏,史其信.基于多智能体系统的城市交通控制与诱导集成化研究[J]. 公路交通科技, 2004, 21(5): 109112.
LI R M, SHI Q X. Research on integration of urban traffic control and route guidance based on multi-agent[J]. Journal of Highway and Transportation Research and Development, 2004, 21(5): 109112.
[4] JI Z J, WANG Z D, LIN H, et al. Interconnection topologies for multi-agent coordination under leader-follower framework[J]. Automatica, 2009, 45(12): 28572863.
[5] LIU X Z, JI Z J. Controllability of multiagent systems based on path and cycle graphs[J]. International Journal of Robust and Nonlinear Control, 2018, 28(1), 296309.
[6] 纪志坚. 网络系统的控制与优化[J]. 系统科学与数学, 2015, 35(3): 257.
JI Z J. Optimization and control of network systems[J]. Journal of Systems Science and Mathematical Sciences, 2015, 35(3): 257.
[7] 王潇, 纪志坚. 基于MAS的无人机新型编队算法[J]. 复杂系统与复杂性科学, 2019, 16(2): 6068.
WANG X, JI Z J. A new UAV formation algorithm based on MAS[J]. Complex Systems and Complexity Science,2019, 16(2): 6068.
[8] ZHAO B, GUAN Y Q. Data-sampling controllability of multi-agent systems[J]. IMA Journal of Mathematical Control and Information, 2020,37(3): 794813.
[9] 国俊豪, 纪志坚. 基于NE结果的多智能体系统模型及其能控性[J]. 复杂系统与复杂性科学, 2021, 18(4): 5057.
GUO J H, JI Z J. A multi-agent system model based on NE results and its controllability[J]. Complex Systems and Complexity Science, 2021, 18(4): 5057.
[10] 张志伟, 纪志坚. 有向路径下的一类多智能体系统的能控性分析[J]. 复杂系统与复杂性科学, 2022, 19(2): 6370,95.
ZHANG Z W, JI Z J. Controllability of multi-agent system based on directed paths[J]. Complex Systems and Complexity Science, 2022, 19(2): 6370,95.
[11] 纪志坚. 等价划分下多智能体系统能控性的一种判定方法[J/OL]. 聊城大学学报(自然科学版), 2023, 36(6): 18.
JI Z J. A method for determining the controllability of multi-agent systems under equitable partition[J/OL]. Journal of Liaocheng University(Nat Sci), 2023, 36(6): 18.
[12] SU M M, JI Z J, LIU Y G, et al. Improved multi-agent controllability processing technique based on equitable partition[J]. ISA Transactions, 2023, 138: 301310.
[13] GUAN Y Q, JI Z J, ZHANG L, et al. Controllability of multi-agent systems under directed topology[J]. International Journal of Robust and Nonlinear Control, 2017, 27(18): 43334347.
[14] QU J J, JI Z J, SHI Y. The graphical conditions for controllability of multiagent systems under equitable partition[J]. IEEE Transactions on Cybernetics, 2021, 51(9): 46614672.
[15] ZHAO L H, JI Z J, LIU Y G, et al. Controllability of general linear discrete multi-agent systems with directed and weighted signed network[J]. Journal of Systems Science and Complexity, 2022, 35(6): 21072130.
[16] GUO J H, JI Z J, LIU Y G, et al. Unified understanding and new results of controllability model of multi-agent systems[J]. International Journal of Robust and Nonlinear Control, 2022, 32(11): 63306345.
[17] JI Z J, LIU H, YU H S. Leaders in multi-agent controllability under consensus algorithm and tree topology[J]. Systems and Control Letters, 2012, 61(9), 918925.
[18] SU H S, LONG M K, ZENG Z G. Controllability of two-time-scale discrete-time multiagent systems[J]. IEEE Transactions on Cybernetics, 2020, 50(4): 14401449.
[19] JI Z J, WANG L, GUO X X. On controllability of switched linear systems[J]. IEEE Transactions on Automatic Control, 2008, 53(3): 796801.
[20] SUN Z D, ZHENG D H. On reachability and stabilization of switched linear systems[J]. IEEE Transactions on Automatic Control, 2001, 46(2): 291295.
[21] SUN Z D, GE S S, LEE T H. Controllability and reachability criteria for switched linear systems[J]. Automatica, 2002, 38(5): 775786.
[22] XIE G M, WANG L. Controllability and stabilizability of switched linear-systems[J]. Systems and Control Letters, 2003, 48(2): 135155.
[23] CHENG D Z. Controllability of switched bilinear systems[J]. IEEE Transactions on Automatic Control, 2005, 50(4): 511515.
[24] JI Z J, WANG Z D, LIN H, et al. Controllability of multi-agent systems with time-delay in state and switching topology[J]. International Journal of Control, 2010, 83(2): 371386.
[25] LIU B, CHU T G, WANG L, et al. Controllability of switching networks of multi-agent systems[J]. International Journal of Robust and Nonlinear Control, 2012, 22(6): 630644.
[26] JI Z J, WANG L, GUO X X. Design of switching sequences for controllability realization of switched linear systems[J]. Automatica, 2007, 43(4): 662668.
[27] TIAN L L, ZHAO B, WANG L. Controllability of multi-agent systems with periodically switching topologies and switching leaders[J]. International Journal of Control, 2018, 91(5): 10231033.
[28] TIAN L L, GUAN Y Q, WANG L. Controllability and observability of switched multi-agent systems[J]. International Journal of Control, 2019, 92(8): 17421752.
[29] 司元超. 时滞多智能体系统的能控性研究[D]. 贵州:贵州大学, 2022.
SI Y C. Research on controllability of multi-agent systems with delay[D]. Guizhou: Guizhou University, 2022.
[30] 张婷瑞. 随机切换系统的纳什均衡精确能控性及线性二次最优控制[D]. 北京:北京交通大学, 2018.
ZHANG T R. Nash equilibrium precision controllability and linear quadratic optimal control for stochastic switched systems[D]. Beijing: Beijing Jiaotong University, 2018.
[31] LI A M, CORNELIUS S P, LIU Y Y, et al. The fundamental advantages of temporal networks[J]. Science, 2017, 358(6366): 10421046.

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献