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.
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.
CHEN Yingxin, JI Zhijian. Controllability of Multi-agent Under Switching Pseudo-paths[J]. Complex Systems and Complexity Science, 2025, 22(2): 135-144.
[1] TANNER H. On the controllability of nearest neighbor interconnections[C]//Proceedings of the 43rd 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.