# Article

Full entry | PDF   (0.3 MB)
Keywords:
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.
References:
[1] Fax, A., Murray, R.: Information flow and cooperative control of vehicle formations. IEEE Trans. Automat. Control 49 (2004), 1465–1476. DOI 10.1109/TAC.2004.834433 | MR 2086912
[2] Gao, L., Yuan, H., Jin, D.: Consensus problems in multi-agent systems with double integrator model. Chinese Physical B, 19 (2010) 050520. DOI 10.1088/1674-1056/19/5/050520
[3] Godsil, C., Royle, G.: Algebraic Graph Theory. Springer-Verlag, New York 2001. MR 1829620 | Zbl 0968.05002
[4] Gu, K., Kharitonov, V., Chen, J.: Stability of Time-Delay Systems. Springer Verlag, Boston 2003. Zbl 1039.34067
[5] Hale, J., Lunel, S. V.: Introduction to Theory of Functional Differential Equations. Springer, New York 1991.
[6] Hong, Y., Chen, G., Bushnell, L.: Distributed observers design for leader-following control of multi-agent networks. Automatica 44 (2008), 846–850. DOI 10.1016/j.automatica.2007.07.004 | MR 2527101
[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. DOI 10.1016/j.automatica.2006.02.013 | MR 2230987 | Zbl 1117.93300
[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. DOI 10.1007/s11424-009-9197-z | MR 2565265
[9] Horn, R., Johnson, C.: Matrix Analysis. Cambridge Univ. Press, New York 1985. MR 0832183 | Zbl 0576.15001
[10] Hu, J.: On robust consensus of multi-agent systems with communicaiton delays. Kybernetika 5 (2009), 768–784. MR 2599111
[11] Hu, J., Feng, G.: Distributed tracking control of leader-follower multi-agent systems under noisy measurement. Automatica 46 (2010), 1382–1387. DOI 10.1016/j.automatica.2010.05.020 | MR 2877254 | Zbl 1204.93011
[12] Hu, J., Hong, Y.: Leader-following coordination of multi-agent systems with coupling time delays. Physica A 37 (2007), 853–863.
[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.
[14] Murray, R. M.: Recent research in cooperative control of multivehicle systems. ASME J. Dynamic Systems, Measurement, and Control 129 (2007), 571–583. DOI 10.1115/1.2766721
[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. DOI 10.1109/TAC.2004.834113 | MR 2086916
[16] Ren, W., Beard, R. W.: Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Applications. Springer, Berlin 2008. Zbl 1144.93002
[17] Sontag, E.: On the input-to-state stability property. European J. Control 1 (1995), 24–36. DOI 10.1016/S0947-3580(95)70005-X | Zbl 1177.93003
[18] Teel, A.: Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem. IEEE Trans. Automat. Control 45 (1998), 960–964. DOI 10.1109/9.701099 | MR 1633496 | Zbl 0952.93121
[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. DOI 10.1109/TAC.2010.2076250 | MR 2767160

Partner of