Abstract：This paper investigates the herdability of multi-agent systems with general linear and signed matrix-weighted networks under signed directed graphs. Firstly, we present the sufficient conditions for herdability of general linear multi-agent systems by utilizing controllability structure decomposition. Moreover, leveraging the concepts of controllable subspaces and graph theory, we propose a set of graph-theoretic conditions for the herdability of multi-agent systems under different matrix weight scenarios. Finally, we introduce the definition of signed matrix-weighted distance-equivalent partitioning and provide the herdability criteria for general matrix-weighted networks under this partitioning. It is found that the system is herdable when the non-zero elements of the weight matrix are either all positive or all negative.
朱佳慧, 纪志坚, 国俊豪. 符号矩阵权重多智能体的可聚集性[J]. 复杂系统与复杂性科学, 2026, 23(4): 91-98.
ZHU Jiahui, JI Zhijian, GUO Junhao. Herdability of Multi-agent Systems with Signed Matrix-weighted Networks[J]. Complex Systems and Complexity Science, 2026, 23(4): 91-98.
[1] Ji Z J, Yu H S. A newperspective to graphical characterization of multiagent controllability[J]. IEEE Transactions on Cybernetics, 2017, 47(6): 1471-1483. [2] Ruf S F, Egerstedt M, Shamma J S, et al. Herdability of linear systems based on sign patterns and graph structures[J]. CoRR, 2019, abs/1904. 08778. [3] Claudio A. Consensus problems on networks with antagonistic interactions[J]. IEEE Trans Automat Contr, 2013, 58(4): 935-946. [4] Amirreza R, Meng J, Mesbahi M, et al. Controllability of multi-agent systems from a graph-theoretic perspective[J]. SIAM Journal on Control and Optimization, 2009, 48(1): 162-186. [5] Guan Y Q, Tian L L, Wang L. Controllability of switching signed networks[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2019, 67(6): 1-1. [6] She B K, Kan Z. Characterizing controllable subspace and herdability of signed weighted networks via graph partition[J]. Automatica, 2020, 115: 108900. [7] De P G, Valcher M E. On the herdability of linear time-invariant systems with special topological structures[J]. Automatica, 2023, 149: 110804. [8] She B K, Cai M Y, Kan Z. Characterizing herdability of signed networks via graph walks[C]//Proceedings of 2019 58th IEEE Conference on Decision and Control. Nice, France: IEEE, 2019: 5456-5461. [9] Siddhartha M, She B K, Gao H, et al. Leader group selection for herdability of structurally balanced signed networks[C]//2020 59th IEEE Conference on Decision and Control. Jeju, Korea (South), 2020: 5567-5572. [10] 魏静, 关永强, 谌煜, 等. 基于领导者选择的聚类平衡网络的可牧性[J]. 控制与决策, 2025, 40(4): 1386-1394. Wei J, Guan Y Q, Shen Y, et al. Herdability of clustering balanced networks based on leader selection[J]. Control and Decision, 2025, 40(4): 1386-1394. [11] Auletta, Fabrizia, Richardson M J, et al. Herding stochastic autonomous agents via local control rules and online target selection strategies[J]. Autonomous Robots, 2022, 46(3): 469-491. [12] Sun Y S, Ji Z J, Liu Y G, et al. On stabilizability of multi-agent systems[J]. Automatica, 2022, 144: 110491. [13] Liu B, Su H S, Wu L C, et al. Controllability for multi-agent systemswith matrix-weight based signed network[J]. Applied Mathematics and Computation, 2021, 411: 126520. [14] Pan L, Shao H, Mesbahi M, et al. On the controllability of matrix-weighted networks[J]. IEEE Control Systems Letters, 2020, 4(3): 572-577. [15] Tuna S E. Observability through a matrix-weighted graph[J]. IEEE Transactions on Automatic Control, 2018, 63(7): 2061-2074. [16] Trinh M H, Nguyen C V, Lim Y H, et al. Matrix weighted consensus and its applications[J]. Automatica, 2018, 89: 415-419. [17] Qu J J, Ji Z J, Shi Y, et al. The graphical conditions for controllability ofmult-agent systems under equitable partition[J]. IEEE Transactions on Cybernetics, 2021, 51(9): 4661-4672. [18] Lorenzo F, Sergio R. Positive Linear Systems: Theory and Applications[M]. Hoboken, NJ, USA: John Wiley and Sons, Inc, 2000. [19] Godsil C, Royle G F. Algebraic Graph Theory[M]. Berlin: Springer Science and Business Media, 2001: 1-427. [20] Aguilar O C, Gharesifard B. Graph controllability classes for the Laplacian leader-follower dynamics[J]. IEEE Trans Automat Contr, 2015, 60(6): 1611-1623.
