Containment Control for Multi-Agent System with Multiple Stationary Leaders and Time-Delays
LI Bo1, CHEN Zengqiang1,2, LIU Zhongxin1, ZHANG Qing2
1. College of Computer & Control Engineering, Nankai University, Tianjin 300071, China; 2.College of Science, Civil Aviation University of China, Tianjin 300300, China
Abstract：This paper is concerned with distributed containment control of multi-agent system with multiple stationary leaders under fixed directed network topologies. Under the assumption that communication time-delays in all channels are equal, the Laplace transform is used to study the first-order and second-order multi-agent delayed system with continuous-time. Some sufficient conditions are obtained to ensure the containment of the multi-agent system by stability analysis for transfer function to get conditions and applying final value theorem. Finally,computer simulations show the effectiveness of the conclusion.
李勃, 陈增强, 刘忠信, 张青. 含时延的多智能体系统的多静态领导者包容控制[J]. 复杂系统与复杂性科学, 2016, 13(2): 105-110.
LI Bo, CHEN Zengqiang, LIU Zhongxin, ZHANG Qing. Containment Control for Multi-Agent System with Multiple Stationary Leaders and Time-Delays[J]. Complex Systems and Complexity Science, 2016, 13(2): 105-110.
[1] Reynolds C W.Flocks,herds and schools a distributed behavioral model[J].Computer Graphics,1987,21(4):25-34. [2] Vicsek T, Czirok A, Ben Jacob E, et al. Novel type ofphase transition in a system of self-driven particles[J].Physical Review Letters,1995,75(6):1226-1229. [3] Jadbabaie A, Lin J, Morse A S. Coordination of groupsof mobile agents using nearest neighbor rules[J].IEEETranson Automatic Control,2003,48(6):988-1001. [4] Moreau L.Stability of multi-agent systems with timedependent communication links[J].IEEE Trans onAutomatic Control,2005,50(2):169-182. [5] Ren W, Beard R W.Consensus seeking in multi-agentsystems under dynamically changing interactiontopologies[J].IEEE Trans on Automatic Control,2005,50(5):655-661. [6] JiM,Ferrari-Trecate G, Egerstedt M, et al. Containment control in mobile networks[J].IEEE Transactions onAutomatic Control,2008,53(8):1972-1975. [7] 于镝,白丽娟,李铖.非线性多智能体网络的分布式包容控制[J].复杂系统与复杂性科学,2013,10(2):63-68. Yu Di, Bai LiJuan, Li Cheng. Distributed containment control of nonlinear multi-agent networks[J].Complex Systems and Complexity Science,2013,10(2):63-68. [8] Dong X W,Meng F L,Shi Z Y,et al. Output containment control for swarm systems with general lineardynamics: a dynamic output feedback approach[J].Systems & Control Letters,2014(71):31-37. [9] Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays[J].IEEE Transaction on Automatic Control,2004,49(9):1520-1533. [10] Yu W W,Chen G R,Cao M. Some necessary and sufficient conditions for second-order consensus inmulti-agent dynamical systems[J].Automatica,2010,46(6):1089-1095. [11] 杨洪勇,张嗣瀛. 离散时间系统的多智能体的一致性[J].控制与决策,2009,24(3):413-416. Yang Hongyong, Zhang SiYing.Consensus of multi-agent system with discrete-time[J].Control and Decision, 2009,24(3):413-416. [12] Xia C Y, Wang Z, Sanz J, et al.Effects of delayed recovery and nonuniform transmission on the spreading of diseases in complex networks[J].Physica A, 2013(392): 1577-1585. [13] Wang L, Sun S W, Xia C Y. Finite-time stability of multi-agent system in disturbed environment[J].Nonlinear Dynamics,2012,(67):2009-2016. [14] Xia C Y, Wang L, Sun S W,et al.An SIR model with infection delay and propagation vector in complex networks[J].Nonlinear Dynamics,2012(69): 927-934. [15] Liu K E, Xie G M, Wang L.Containment control for second-order multi-agent systems withtime-varying delays[J].Systems & Control Letters,2014(67):24-31. [16] Cao Y C,Ren W,Egerstedt M.Distributed containment control with multiple stationary or dynamic leaders infixed and switching directed networks[J].Automatica, 2012, 48(8): 1586-1597. [17] Rockafellar R T. Convex Analysis[M].New Jersey:Princeton University Press,1972. [18] Ren W, Cao Y C.Distributed Coordination of Multi-agent Networks[M].London:Springer, 2011. [19] Liu H, Xie G M, Wang L. Necessary and sufficient conditions for containmentcontrol of networked multi-agent systems[J].Automatica,2012,48(7):1415-1422. [20] 胡寿松.自动控制原理[M].5版.北京:科学出版社,2006:636-637.
