L. Galbusera, M.P.E. Marciandi, P. Bolzern, and G. Ferrari-Trecate. Control schemes based on the wave equation for consensus in multi-agent systems with double-integrator dynamics. Proc. 46th IEEE Conference on Decision and Control , pages 1498--1503, 2007. New Orleans, LA, US, 12-14 December.
In this paper, we consider the problem of drivinga group of agents communicating through an undirected andweighted network towards a consensus point. We assume thatagents obey to double-integrator dynamics and study decentralizedcontrol schemes for consensus of the position variables. Inparticular we revisit control policies proposed in (Xie and Wang, 2007) and (Ren and Atkins, 2005)in the unified framework of Partial difference Equations overgraphs and highlight the link between the closed-loop systemdynamics and the damped wave equation describing the motionof a free elastic beam.