Previous |  Up |  Next


Title: Consensus seeking in multi-agent systems with an active leader and communication delays (English)
Author: Gao, Lixin
Author: Tang, Yutao
Author: Chen, Wenhai
Author: Zhang, Hui
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 47
Issue: 5
Year: 2011
Pages: 773-789
Summary lang: English
Category: math
Summary: In this paper, we consider a multi-agent consensus problem with an active leader and variable interconnection topology. The dynamics of the active leader is given in a general form of linear system. The switching interconnection topology with communication delay among the agents is taken into consideration. A neighbor-based estimator is designed for each agent to obtain the unmeasurable state variables of the dynamic leader, and then a distributed feedback control law is developed to achieve consensus. The feedback parameters are obtained by solving a Riccati equation. By constructing a common Lyapunov function, some sufficient conditions are established to guarantee that each agent can track the active leader by assumption that interconnection topology is undirected and connected. We also point out that some results can be generalized to a class of directed interaction topologies. Moreover, the input-to-state stability (ISS) is obtained for multi-agent system with variable interconnection topology and communication delays in a disturbed environment. (English)
Keyword: multi-agent system
Keyword: consensus
Keyword: leader-following
Keyword: time-delay
MSC: 62A10
MSC: 93E12
idZBL: Zbl 1236.93006
idMR: MR2850463
Date available: 2011-11-10T15:44:48Z
Last updated: 2013-09-22
Stable URL:
Reference: [1] Fax, A., Murray, R.: Information flow and cooperative control of vehicle formations.IEEE Trans. Automat. Control 49 (2004), 1465–1476. MR 2086912, 10.1109/TAC.2004.834433
Reference: [2] Gao, L., Yuan, H., Jin, D.: Consensus problems in multi-agent systems with double integrator model.Chinese Physical B, 19 (2010) 050520. 10.1088/1674-1056/19/5/050520
Reference: [3] Godsil, C., Royle, G.: Algebraic Graph Theory.Springer-Verlag, New York 2001. Zbl 0968.05002, MR 1829620
Reference: [4] Gu, K., Kharitonov, V., Chen, J.: Stability of Time-Delay Systems.Springer Verlag, Boston 2003. Zbl 1039.34067
Reference: [5] Hale, J., Lunel, S. V.: Introduction to Theory of Functional Differential Equations.Springer, New York 1991.
Reference: [6] Hong, Y., Chen, G., Bushnell, L.: Distributed observers design for leader-following control of multi-agent networks.Automatica 44 (2008), 846–850. MR 2527101, 10.1016/j.automatica.2007.07.004
Reference: [7] Hong, Y., Hu, J., Gao, L.: Tracking control for multi-agent consensus with an active leader and variable topology.Automatica 42 (2006), 1177–1182. Zbl 1117.93300, MR 2230987, 10.1016/j.automatica.2006.02.013
Reference: [8] Hong, Y., Wang, X.: Multi-agent tracking of a high-dimensional active leader with switching topology.J. Syst. Sci. Complex. 22 (2009), 722–731. MR 2565265, 10.1007/s11424-009-9197-z
Reference: [9] Horn, R., Johnson, C.: Matrix Analysis.Cambridge Univ. Press, New York 1985. Zbl 0576.15001, MR 0832183
Reference: [10] Hu, J.: On robust consensus of multi-agent systems with communicaiton delays.Kybernetika 5 (2009), 768–784. MR 2599111
Reference: [11] Hu, J., Feng, G.: Distributed tracking control of leader-follower multi-agent systems under noisy measurement.Automatica 46 (2010), 1382–1387. Zbl 1204.93011, MR 2877254, 10.1016/j.automatica.2010.05.020
Reference: [12] Hu, J., Hong, Y.: Leader-following coordination of multi-agent systems with coupling time delays.Physica A 37 (2007), 853–863.
Reference: [13] Luo, Y., Gao, L., Wang, F.: The $L_2-L_{\infty }$ control for leader-following coordination with switching topology and time-delay.J. Networks 5 (2010), 1513–1520.
Reference: [14] Murray, R. M.: Recent research in cooperative control of multivehicle systems.ASME J. Dynamic Systems, Measurement, and Control 129 (2007), 571–583. 10.1115/1.2766721
Reference: [15] Olfati-Saber, R., Murray, R. M.: Consensus problems in networks of agents with switching topology and time-delays.IEEE Trans. Automat. Control, 49 (2004), 1520–1533. MR 2086916, 10.1109/TAC.2004.834113
Reference: [16] Ren, W., Beard, R. W.: Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Applications.Springer, Berlin 2008. Zbl 1144.93002
Reference: [17] Sontag, E.: On the input-to-state stability property.European J. Control 1 (1995), 24–36. Zbl 1177.93003, 10.1016/S0947-3580(95)70005-X
Reference: [18] Teel, A.: Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem.IEEE Trans. Automat. Control 45 (1998), 960–964. Zbl 0952.93121, MR 1633496, 10.1109/9.701099
Reference: [19] Wang, X., Hong, Y., Huang, J., Jiang, Z.: A distributed control approach to a robust output regulation problem for linear systems.IEEE Trans. Automat. Control 55 (2010), 2891–2896. MR 2767160, 10.1109/TAC.2010.2076250


Files Size Format View
Kybernetika_47-2011-5_9.pdf 350.6Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo