[1]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]
Copy
Controllability analysis of multi-agent systems based on topological structure and individual dynamic level
CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume:
15
Number of periods:
2020 2
Page number:
264-270
Column:
学术论文—智能系统
Public date:
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
- CLC:
- TP273
- DOI:
- 10.11992/tis.201901006
- 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.
- 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.
- Similar References:
Memo
-
Last Update:
1900-01-01