Previous |  Up |  Next


state-dependent graph; Lasalleś Invariant Principle; dynamic system
Recent years have witnessed an increasing interest in coordinated control of distributed dynamic systems. In order to steer a distributed dynamic system to a desired state, it often becomes necessary to have a prior control over the graph which represents the coupling among interacting agents. In this paper, a simple but compelling model of distributed dynamical systems operating over a dynamic graph is considered. The structure of the graph is assumed to be relied on the underling system's states. Then by following a proper protocol, the state-dependent dynamic graph is driven to a pre-specified structure. The main results are derived via Lasalle's Invariant Principle and numerical examples that find very good agreements with the analytical results are also included.
[1] L. Conradt and T. J. Roper: Consensus decision making in animals. Trends Ecol. Evol. 20 (2005), 450–456.
[2] D. V. Dimarogonas and K. J. Kyriakopoulos: On the rendezvous problem for multiple nonholonomic agents. IEEE Trans. Automat. Control 52 (2007), 5, 916–922. MR 2324255
[3] N. R. Franks, A. Dornhaus, J. P. Fitzsimmons, and M. Stevens: Speed versus accuracy in collective decision making. Proc. Roy. Soc. London Ser. B 270 (2003), 270, 2457–2463.
[4] Y. Hatano and M. Mesbahi: Agreement over random networks. IEEE Trans. Automat. Control 50 (2005), 11, 1867–1872. MR 2182742
[5] A. Jadbabaie, J. Lin, and A. S. Morse: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control 48 (2003), 6, 988–1001. MR 1986266
[6] S. J. Lu and L. Chen: A general synchronization method of chaotic communication systems via Kalman filtering. Kybernetika 44 (2008), 1, 43–52. MR 2405054
[7] M. Mesbahi: On state-dependent dynamic graphs and their controllability properties. IEEE Trans. Automat. Control 50 (2005), 3, 387–392. MR 2123101
[8] L. Moreau: Stability of multiagent systems with time-dependent communication links. IEEE Trans. Automat. Control 50 (2005), 2, 169–182. MR 2116423
[9] T. Vicsek, A. Cziroäok, E. Ben-Jacob, I. Cohen, and O. Shochet: Novel type of phase transition in a system of self-deriven particles. Phys. Rev. Lett. 75 (1995), 6, 1226–1229.
[10] M. M. Zavlanos and G. J. Pappas: Controlling connectivity of dynamic graphs. In: IEEE Conf. on Decision and Control and European Control Conference, Seville 2005, p. 6.
Partner of
EuDML logo