为基于纳什均衡的结果得到多智能体系统的一类新模型,结合实际并运用图论的方法,构造了一类不同于一般模型和Tanner模型的新模型——等邻居模型,该模型首次将纳什均衡与图拓扑结构建立联系。分析了等邻居模型与其他模型在多智能体系统中所得到的能控性的不同点,并发现等邻居模型在特定条件下能够与其他模型产生相同的能控性。
It is very meaningful to get a new model of multi-agent system based on Nash equilibrium. Combining the practice and using the graph theory method, this paper constructs a new class of model which is different from the general model and Tanner model: iso-neighbor model. We first introduce the unique characteristics of this kind of model from the point of view of graph theory, then analyze the differences of controllability between iso-neighbor model and other models in multi-agent system, and draw the following conclusions: The iso-neighbor model can produce the same controllability as other models under fixed conditions.
[1]Liu K E, Ji Z J, Xie G M, et al. Event-based broadcasting containment control for multi-agent systems under directed topology[J]. International Journal of Control, 2016, 89(11): 2360-2370.
[2]Guan Y Q, Ji Z J, Zhang L, et al. Controllability of heterogeneous multi-agent systems under directed and weighted topology[J]. International Journal of Control, 2016, 89(5): 1009-1024.
[3]Li Z Q, Ji Z J, Chao Y C, et al. Graph controllability classes of networked multi-agent systems with multi-signal inputs[J].CAAI Transactions on Intelligent Systems, 2016, 11(5): 783-790.
[4]Ji Z J, Lin H, Yu H S. Protocols design and uncontrollable topologies construction for multi-agent networks[J]. IEEE Transactions on Automatic Control, 2015, 60(3): 781-786.
[5]Ji Z J, Lin H, Feng G, et al. Controllability structure decomposition for switched linear systems[J]. Transactions of the Institute of Measurement and Control, 2010, 32(6): 736-755.
[6]Liu B, Ping Y, Wu L, et al. Controllability of discrete-time multi-agent systems based on absolute protocol with time-delays[J].Neurocomputing, 2020, 409(2020): 316-328.
[7]Liu B, Su H, Wu L,et al. Fractional-order controllability of multi-agent systems with time-delay. [DB/OL]. (2020-04-05)[2021-01-10]. https:∥sci-hub.se/10.1016/j.neucom.2020.04.083.
[8]Cesar O, Bahman G. Graph controllability classes for the laplacian leader-follower dynamics[J]. IEEE Transactions on Automatic Control, 2015, 60(6):1611-1623.
[9]Tanner H. On the controllability of nearest neighbor interconnections[J]. Proceedings of the 43rd IEEE Conference on Decision and Control. Atlantis, Raradise Island, Bahamas, 2004: 2467-2472.
[10] Wang L, Jiang F C, Xie G M. Controllability of multi-agent systems based on agreement protocols[J]. Sci China Ser F-Inf Sci, 2009, 52(11): 2074-2088.
[11] Cardoso D M, Delorme M, Rama P. Laplacian eigenvectors and eigenvalues and almost equitable partitions[J]. European Journal of Combinatorics, 2007, 28(3): 665-673.
[12] Qu J J, Ji Z J, Shi Y. The graphical conditions for controllability of multi-agent systems under equitable partition[DB/OL].(2020-05-24)[2021-01-10]. https:∥www.ieee.org/publications/rights/index.html.
[13] Zhang R R, Guo L. Controllability of nash equilibrium in game-based control systems[J]. IEEE Transactions on Automatic Control, 2019, 64(10): 4180-4187.
[14] Ma J Y, Zheng Y S, Zhou L K. Game-based coalescence in multi-agent systems[DB/OL].(2020-05-24)[2021-01-10].https:∥doi.org/10.1016/j.syseonle. 2020.104853.
[15] 郑大钟,线性系统理论[M]. 北京:清华大学出版社, 2002:135-208.
[16] Sun C, Hu G, Xie L. Controllability of multiagent networks with antagonistic interactions[J]. IEEE Transactions on Automatic Control, 2017, 62(10): 5457-5462.
[17] She B, Mehta S, Ton C, et al. Controllability ensured leader group selection on signed multiagent networks[J]. IEEE Transactions on Cybernetics, 2020, 50(1): 222-232.
[18] Ji Z J, Wang Z D, Lin H, et al. Interconnection topologies for multi-agent coordination under leader-follower framework[J]. IEEE Trans Autom, 2009, 45(12): 2857-2863.