[1]陈万金,纪志坚.基于拓扑结构和个体动态层面的多智能体系统可控性分析[J].智能系统学报,2020,15(2):264-270.[doi:10.11992/tis.201901006]
CHEN Wanjin,JI Zhijian.Controllability analysis of multi-agent systems based on topological structure and individual dynamic level[J].CAAI Transactions on Intelligent Systems,2020,15(2):264-270.[doi:10.11992/tis.201901006]
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CHEN Wanjin,JI Zhijian.Controllability analysis of multi-agent systems based on topological structure and individual dynamic level[J].CAAI Transactions on Intelligent Systems,2020,15(2):264-270.[doi:10.11992/tis.201901006]
基于拓扑结构和个体动态层面的多智能体系统可控性分析
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
15
期数:
2020年第2期
页码:
264-270
栏目:
学术论文—智能系统
出版日期:
2020-03-05
- Title:
- Controllability analysis of multi-agent systems based on topological structure and individual dynamic level
- Keywords:
- multi-agent system; controllability; linear time-invariant systems; topology; local interaction; eigenvalue; eigenvector; control theory
- 分类号:
- TP273
- 摘要:
- 针对一般线性多智能体系统中网络拓扑及个体动态这两个层面的可控性对系统整体可控性的关系进行了研究，提出了一种新的描述一般线性多智能体系统的模型。利用PBH(Popov-Belevitch-Hautus)判据，得到并证明了在此模型下多智能体系统可控性在网络拓扑结构与个体动态层面的充要条件。结合具体的例子解释了系统矩阵中出现重复特征值时对定理2充分性的影响，并且提供了一种避免重复特征值出现的方法。特别地，推导出了此模型下系统矩阵为实对称矩阵这一特殊情况时可以判定该系统不可控的两种判定条件，即比较系统矩阵中最大的特征值代数重数与控制矩阵中1元素的个数，满足条件即判定系统不可控。
- Abstract:
- The relationship between the controllability of network topology and individual dynamics in the overall controllability of the system is studied, and a new model describing the general linear multi-agent system is proposed. Using the Popov-Belevitch-Hautus (PBH) criterion, the necessary and sufficient conditions for the controllability of a multi-agent system in the network topology and individual dynamic level are obtained and proved, and the effect of repeated eigenvalues in the system matrix on the sufficiency of Theorem 2 is explained with a concrete example. We provide a way to avoid the occurrence of repeated eigenvalues. In particular, the two conditions for judging the uncontrollable system can be determined when the system matrix is a real symmetric matrix under this model; that is, compare the largest eigenvalue algebraic multiplicity in the system matrix with the number of 1 elements in the control matrix. If this condition is satisfied, the system is uncontrollable.
- 参考文献/References:
-
[1] XIE Guangming, WANG Long. Consensus control for a class of networks of dynamic agent[J]. International journal of robust and nonlinear control, 2007, 17(10/11): 941-959.
[2] XIAO Feng, WANG Long, CHEN Jie, et al. Finite- time formation control for multi-agent systems[J]. Automatica, 2009, 45(11): 2605-2611.
[3] 王晓晓, 纪志坚. 广播信号下非一致多智能体系统的能控性[J]. 智能系统学报, 2014, 9(4): 401-406
WANG Xiaoxiao, JI Zhijian. Controllability of non-identical multi-agent systems under a broadcasting control signal[J]. CAAI transactions on intelligent systems, 2014, 9(4): 401-406
[4] ZHENG Y, ZHU Y, WANG L. Consensus of heterogeneous multi-agent systems[J]. IET control theory and applications, 2011, 5(16): 1881-1888.
[5] ADLER J L, SATAPATHY G, MANIKONDA V, et al. A multi-agent approach to cooperative traffic management and route guidance[J]. Transportation research part B: methodological, 2005, 39(4): 297-318.
[6] 单素素, 纪志坚, 翟海川. 采用Leader-follower和模糊反馈机制的机器鱼队形控制[J]. 智能系统学报, 2013, 8(3): 247-253
SHAN Susu, JI Zhijian, ZHAI Haichuan. The formation control of multi-robot fish based on leader-follower and fuzzy feedback mechanism[J]. CAAI transactions on intelligent systems, 2013, 8(3): 247-253
[7] 王耀威, 纪志坚, 翟海川. 仿生机器鱼运动控制方法综述[J]. 智能系统学报, 2014, 9(3): 276-284
WANG Yaowei, JI Zhijian, ZHAI Haichuan. A survey on motion control of the biomimetic robotic fish[J]. CAAI transactions on intelligent systems, 2014, 9(3): 276-284
[8] DIMAROGONAS D V, TSIOTRAS P, KYRIAKOPOULOS K J. Leader-follower cooperative attitude control of multiple rigid bodies[J]. Systems and control letters, 2009, 58(6): 429-435.
[9] KALMAN R E. Contributions to the theory of optimal control[J]. Boletin de la sociedad matematica mexicana, 1960, 5: 102-119.
[10] KALMAN R E, HO Y C, NARENDRA K S. Controllability of linear dynamical systems[J]. Contributions to differential equations, 1963, 1(2): 189-213.
[11] TANNER H G. On the controllability of nearest neighbor interconnections[C]//Proceedings of the 43rd IEEE Conference on Decision and Control. Nassau, Bahamas, 2004: 2467-2472.
[12] 关永强, 纪志坚, 张霖, 等. 多智能体系统能控性研究进展[J]. 控制理论与应用, 2015, 32(4): 421-431
GUAN Yongqiang, JI Zhijain, ZHANG Lin, et al. Recent developments on controllability of multi-agent system[J]. Control theory and applications, 2015, 32(4): 421-431
[13] 董洁, 纪志坚, 王晓晓. 多智能体网络系统的能控性代数条件[J]. 智能系统学报, 2015, 10(5): 747-754
DONG Jie, JI Zhijian, WANG Xiaoxiao. Algebraic conditions for the controllability of multi-agent systems[J]. CAAI transactions on intelligent systems, 2015, 10(5): 747-754
[14] JI Zhijian, LIN Hai, YU Haisheng. Leaders in multi-agent controllability under consensus algorithm and tree topology[J]. Systems and control letters, 2012, 61(9): 918-925.
[15] JI Zhijian, LIN Hai, YU Haisheng. Protocols design and uncontrollable topologies construction for multi-agent networks[J]. IEEE transactions on automatic control, 2015, 60(3): 781-786.
[16] JI Zhijian, WANG Zidong, LIN Hai, et al. Interconnection topologies for multi-agent coordination under leader-follower framework[J]. Automatica, 2009, 45(12): 2857-2863.
[17] 晁永翠, 纪志坚, 王耀威, 等. 复杂网络在路形拓扑结构下可控的充要条件[J]. 智能系统学报, 2015, 10(4): 577-582
CHAO Yongcui, JI Zhijian, WANG Yaowei, et al. Necessary and sufficient conditions for the controllability of complex networks with path topology[J]. CAAI transactions on intelligent systems, 2015, 10(4): 577-582
[18] SCHOLTES I, WIDER N, GARAS A. Higher-order aggregate networks in the analysis of temporal networks: path structures and centralities[J]. The European physical journal B, 2016, 89(3): 61.
[19] CZEIZLER E, WU K C, GRATIE C, et al. Structural target controllability of linear networks[J]. IEEE/ACM transactions on computational biology and bioinformatics, 2018, 15(4): 1217-1228.
[20] LIU Kaien, JI Zhijian. Consensus of multi-agent systems with time delay based on periodic sample and event hybrid control[J]. Neurocomputing, 2017, 270: 11-17.
[21] DORIGO M, GAMBARDELLA L M. Ant colony system: a cooperative learning approach to the traveling salesman problem[J]. IEEE transactions on evolutionary computation, 1997, 1(1): 53-66.
[22] JI Meng, EGERSTEDT M. A graph-theoretic characterization of controllability for multi-agent systems[C]//Proceedings of the 2007 American Control Conference. New York, USA, 2007: 4588-4593.
[23] MARTINI S, EGERSTEDT M, BICCHI A. Controllability analysis of multi-agent systems using relaxed equitable partitions[J]. International journal of systems, control and communications, 2010, 2(1/2/3): 100-121.
[24] 张安慧, 张世杰, 陈健, 等. 多智能体系统可控性的图论刻画[J]. 控制与决策, 2011, 26(11): 1621-1626, 1631
ZHANG Anhui, ZHANG Shijie, CHEN Jian, et al. Graph-theoretic characterization of controllability for multi-agent systems[J]. Control and decision, 2011, 26(11): 1621-1626, 1631
[25] AMLIBEL M K, ZHANG S, CAO M. Comments on ‘Controllability analysis of multi-agent systems using relaxed equitable partitions’[J]. International journal of systems, control and communications, 2012, 4(1/2): 72-75.
[26] ZHANG Shuo, CAO Ming, CAMLIBEL M K. Upper and lower bounds for controllable subspaces of networks of diffusively coupled agents[J]. IEEE transactions on automatic control, 2014, 59(3): 745-750.
[27] JI Zhijian, LIN Hai, LEE T H. A graph theory based characterization of controllability for multi-agent systems with fixed topology[C]//Proceedings of the 47th IEEE conference on Decision and control. Cancun, Mexico, 2008: 5262-5267.
[28] LIU Xianzhu, JI Zhijian. Controllability of multiagent systems based on path and cycle graphs[J]. International journal of robust and nonlinear control, 2018, 28(1): 296-309.
[29] 楚天广, 杨正东, 邓奎英, 等. 群体动力学与协调控制研究中的若干问题[J]. 控制理论与应用, 2010, 27(1): 86-93
CHU Tianguang, YANG Zhengdong, DENG Kuiying, et al. Problems in swarm dynamics and coordinated control[J]. Control theory and applications, 2010, 27(1): 86-93
[30] XUE Mengran, ROY S. Comments on “Upper and lower bounds for controllable subspaces of networks of diffusively coupled agents”[J]. IEEE transactions on automatic control, 2017, 63(7): 2306.
[31] XIANG Linying, ZHU J J H, CHEN Fei, et al. Controllability of weighted and directed networks with nonidentical node dynamics[J]. Mathematical problems in engineering, 2013, 2013: 405034.
[32] 徐仲, 张凯院, 陆全, 等. 矩阵论简明教程[M]. 第2版. 北京: 科学出版社, 2005: 155.
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备注/Memo
收稿日期:2019-01-07。
基金项目:国家自然科学基金项目(61873136,61603288,61374062)
作者简介:陈万金，硕士研究生，主要研究方向为多智能体系统;纪志坚，博士，教授，博士生导师，主要研究方向为群体系统动力学与协调控制、复杂网络、切换动力系统的分析与控制、系统生物以及基于网络的控制系统等。主持国家自然科学基金项目4项。发表学术论文110余篇.
通讯作者:纪志坚.E-mail:jizhijian@pku.org.cn
更新日期/Last Update:
1900-01-01