Abstract This paper investigates the affection of automorphism on controllability for the multi-agent systems with leader-follower framework. By using graph theory and matrix theory, we obtain a criterion for determining the existence of automorphism structure of multi-agent systems. Based on the analyzing of automorphism, we point out the relationship between automorphism and controllability of, which provides a method on the aspect of graphics to identify judging the controllability. In addition, this paper also extends the single leader symmetric systems to the multi-leader symmetric systems, which investigates the controllability of leader selection, and provides the directions and methods for further researches on the controllability of complex topological structures
ZHANG Wei,JI Zhijian,QU Jijun. Controllability of Multi-Agent Systems Based on Leader Symmetry[J]. Complex Systems and Complexity Science,
2019, 16(2): 52-59.
Fax J A. Optimal and cooperative control of vehicle formations[D].Pasadena:California Institute Technology,2001.
[2]
Jadbabaie A, Lin J, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules[J].IEEE Trans on Automatic Control, 2003, 48(6): 988-1001.
[3]
Fax J A, Murray R M. Information flow and cooperative control of vehicle formations[J]. IEEE Trans on Automatic Control, 2004, 49(9): 1465-1476.
[4]
Olfti-Saber R, Murray R M. Consensus protocols for networks of dynamic agents[C]//Proc of American Control Conf, Denver, 2003: 951-956.
[5]
Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays[J]. IEEE Trans on Automatic Control, 2004, 49(9):1520-1533.
[6]
Bliman P A, Ferrari-Trecate G. Average consensus problems in networks of agents with delayed communications[J]. Automatica, 2008, 44(8): 1985-1995.
[7]
Ren W, Beard R W. Consensus seeking in multi-agent systems under dynamically changing interaction topologies[J]. IEEE Trans on Automatic Control, 2005,50(5): 655-661.
[8]
Blondel V, Hendrickx J M, Olshevsky A, et al. Convergence in multi-agent coordination, consensus, and flocking[C]//Proc of IEEE Conf Decision and Control,2005 and 2005 Eur Control Conf, Seville,2005: 2996-3000
[9]
Tanner H G. On the controllability of nearest neighbor interconnections[C]//Proc of IEEE Conf Decision and Control, Atlantis, 2004: 2467-2472.
[10]
Rahmani A, Mesbahi M. On the controlled agreement problem[C]//Proc of American Control Conf, Minneapolis,2006: 1376-1381.
[11]
Ji M, Muhammad A, Egerstedt M. Leader-based multi-agent coordination: Controllability and optimal control[C]//Proc of American Control Conf, Minneapolis, 2006: 1358-1363.
[12]
Ji M, Egerstedt M. A graph-theoretic characterization of controllability for multi-agent systems[C]//Proc of American Control Conf, New York, 2007: 4588-4593.
[13]
Liu B, Xie G M, Chu T G, et al. Controllability of interconnected systems via switching networks with a leader[C]//IEEE Int Conf on Systems, Man and Cybernetics,Taipei, 2006: 3912-3916.
[14]
Ji Z J, Lin H, Lee T H. Controllability of multi-agent systems with switching toplogy[C]//IEEE Int Conf on Robotics, Automation and Mechatronics, Chengdu, 2008:421-426.
[15]
Ji Z J, Wang Z D, Lin H, et al. Controllability of multi-agent systems with time-delay in state and switching topology[J].Int J of Control, 2009, 83(2): 371-386.
[16]
Zamani M, Lin H. Structural controllability of multi-agent systems[C]//Proc of American Control Conf, St Louis,2009: 5743-5748.
[17]
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.
[18]
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.
[19]
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 theory characterization of controllability of multi-agent systems[J].Control and decision-making, 2011, 26 (11): 1621-1626, 1631.
[20]
Zhang S, Camlibel M K, Cao M. Controllability of diffusively-coupled multi-agent systems with general and distance regular coupling topologies[C]∥Decision & Control & European Control Conference,IEEE,2011.
[21]
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.
[22]
Xue M, Roy S. Comment on “Upper and lower bounds for controllable subspaces of networks of diffusively-coupled agents”[J]. IEEE Transactions on Automatic Control, 2018,63(7):2306.
[23]
Aguilar C O, Gharesifard B. On almost equitable partitions and network controllability[C]//American Control Conference. IEEE, 2016.
[24]
Aguilar C O,Gharesifard B.Almost equitable partitions and new necessary conditions for network controllability[J].Automatica,2017,80:25-31.
[25]
Ji M, Muhammad A, Egerstedt M. Leader-based multi-agent coordination: Controllability and optimal control[C]//American Control Conference, IEEE, 2006.
[26]
Tanner H. On the controllability of nearest neighbor interconnections[C]//IEEE Conference on Decision & Control, IEEE, 2004.
[27]
Xiang L, Zhu J J H, Chen F, et al. Controllability of weighted and directed networks with nonidentical node dynamics[J]. Mathematical Problems in Engineering, 2013, 2013(3):2996-3000.
[28]
Martini S, Egerstedt M, Bicchi A. Controllability analysis of multi-agent systems using relaxed equitable partitions[J]. Int J of Systems, Control and Communications, 2010, 2(1/2/3): 100-121.
[29]
Ji Z J,Wang Z D, Lin H, et al. Controllability of multi-agent systems with time-delay in state and switching topology[J].Int J of Control, 2009, 83(2): 371-386.
[30]
Guan Y, Ji Z, Zhang L, et al. Controllability of multi-agent systems under directed topology[J]. International Journal of Robust and Nonlinear Control, 2016,89(5):1009-1024.
