[1]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.[doi:10.11992/tis.201411030]
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Algebraic conditions for the controllability of multi-agent systems

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 10 Number of periods: 2015 5 Page number: 747-754 Column: 学术论文—智能系统 Public date: 2015-10-25
Title:
Algebraic conditions for the controllability of multi-agent systems
Author(s):
DONG Jie;  JI Zhijian;  WANG Xiaoxiao
School of Automation Engineering, Qingdao University, Qingdao 266071, China
Keywords:
multi-agent system; structure controllability; exact controllability; relative protocol; absolute protocol; algebraic condition; graph theory; matrix theory
CLC:
TP273
DOI:
10.11992/tis.201411030
Abstract:
Controllability is a key issue in the study of multi-agent systems, especially structural controllability and exact controllability. This paper summarizes the system model and the algebraic conditions for controllability of multi-agent systems. Based on relative and absolute protocols, the algebraic conditions are analyzed systematically for multi-agent system controllability, using graph theory and matrix theory. Going from homogeneous dynamical multi-agent systems to heterogeneous dynamical multi-agent systems, the existing models and algebraic conditions for multi-agent systems are sorted out. The algebraic conditions for controllability of multi-agent systems are improved, and some new algebraic conditions are proposed. The improvement of algebraic controllability conditions for multi-agent system simplifies the calculation greatly.
References:
[1] LIM H, KANG Y, KIM J, et al. Formation control of leader following unmanned ground vehicles using nonlinear model predictive control[C]//IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Singapore, 2009:945-950.
[2] JADBABAIE A, LIN J, MORSE A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules[J]. IEEE Transactions on Automatic Control, 2003, 48(6):988-1001.
[3] FAX J A. Optimal and cooperative control of vehicle formations[M]. Pasadena:California Institute Technology, 2001:1-11.
[4] OLFATI-SABER R, MURRAY R M. Consensus problems in networks of agents with switching topology and time-delays[J]. IEEE Transactions on Automatic Control, 2004, 49(9):1520-1533.
[5] 刘金琨, 尔联洁. 多智能体技术应用综述[J]. 控制与决策, 2001, 16(2):133-140, 180. LIU Jinkun, ER Lianjie. Overview of application of multiagent technology[J]. Control and Decision, 2001, 16(2):133-140, 180.
[6] FAX J A, MURRAY R M. Information flow and cooperative control of vehicle formations[J]. IEEE Transactions on Automatic Control, 2004, 49(9):1465-1476.
[7] OGREN P, FIORELLI E, LEONARD N E. Cooperative control of mobile sensor networks:adaptive gradient climbing in a distributed environment[J]. IEEE Transactions on Automatic Control, 2004, 49(8):1292-1302.
[8] MU S M, CHU T G, WANG L. Coordinated collective motion in a motile particle group with a leader[J]. Physica A:Statistical Mechanics and its Applications, 2005, 351(2-4):211-226.
[9] HONG Y G, HU J P, GAO L X. Tracking control for multi-agent consensus with an active leader and variable topology[J]. Automatica, 2006, 42(7):1177-1182.
[10] SHI H, WANG L, CHU T G. Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions[J]. Physica D:Nonlinear Phenomena, 2006, 213(1):51-65.
[11] LANE D M, MCFADZEAN A G. Distributed problem solving and real-time mechanisms in robot architectures[J]. Engineering Applications of Artificial Intelligence, 1994, 7(2):105-117.
[12] KALMAN R E. Mathematical description of linear dynamical systems[J]. Journal of the Society for Industrial and Applied Mathematics Series A:Control, 1963, 1(2):152-192.
[13] TANNER H G. On the controllability of nearest neighbor interconnections[C]//Proceedings of the 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas, 2004:2467-2472.
[14] RAHMANI A, MESBAHI M. On the controlled agreement problem[C]//Proceedings of the 2006 American Control Conference. Minneapolis, USA, 2006:1376-1381.
[15] RAHMANI A, JI M, 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.
[16] JI M, EGERSTEDT M. A graph-theoretic characterization of controllability for multi-agent systems[C]//Proceedings of the IEEE American Control Conference. New York, USA, 2007:4588-4593.
[17] 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):2857-2863.
[18] DAVISON E J. Connectability and structural controllability of composite systems[J]. Automatica, 1977, 13(2):109-123.
[19] XIANG L Y, ZHU J J H, CHE F, et al. Controllability of weighted and directed networks with nonidentical node dynamics[OL/EB].[2014-01-20] . http://www.hindawi.com/journals/mpe/2013/405034.
[20] 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.
[21] CAI N, CAO J W, LIU M H, et al. On controllability problems of high-order dynamical multi-agent systems[J]. Arabian Journal for Science and Engineering, 2014, 39(5):4261-4267.
[22] LIU B, CHU T G, WANG L, et al. Controllability of a leader-follower dynamic network with switching topology[J]. IEEE Transactions on Automatic Control, 2008, 53(4):1009-1013.
[23] 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):371-386.
[24] ZHANG S, CAO M, 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.
[25] LIU B, SU H S, LI R, et al. Switching controllability of discrete-time multi-agent systems with multiple leaders and time-delays[J]. Applied Mathematics and Computation, 2014, 228:571-588.
[26] YOON M G, ROWLINSON P, CVETKOVI D, et al. Controllability of multi-agent dynamical systems with a broadcasting control signal[J]. Asian Journal of Control, 2014, 16(4):1066-1072.
[27] NI W, WANG X L, XIONG C. Consensus controllability, observability and robust design for leader-following linear multi-agent systems[J]. Automatica, 2013, 49(7):2199-2205.
[28] Yoon M G. Single agent control for cyclic consensus systems[J]. International Journal of Control, Automation and Systems, 2013, 11(2):243-249.
[29] GODSIL C, ROYLE G. Algebraic Graph Theory[M]. New York:Springer, 2001:163-171.
[30] CAI N, ZHONG Y S. Formation controllability of high-order linear time-invariant swarm systems[J]. IET Control Theory & Application, 2010, 4(4):646-654.
[31] CHEN C T. Linear system theory and design[M]. New York:Oxford University Press, 1999:6.
[32] CAI N, CAO J W, KHAN M J. A controllability synthesis problem for dynamic multi-agent systems with linear high-order protocol[J]. International Journal of Control, Automation and Systems, 2014, 12(6):1366-1371.
[33] HORN R A, Johnson C R. Matrix analysis[M]. Cambridge:Cambridge University Press, 1985:11-14.
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