G. Ferrari-Trecate, L. Galbusera, M.P.E. Marciandi, and R. Scattolini. A model predictive control scheme for consensus in multi-agent systems with single-integrator dynamics and input constraints. Proc. 46th IEEE Conference on Decision and Control , pages 1492--1497, 2007. New Orleans, LA, US, 12-14 December.
In this paper we address the problem of drivinga group of agents towards a consensus point when agents havea discrete-time single-integrator dynamics and the communicationgraph is undirected and time-varying. We propose adecentralized Model Predictive Control (MPC) scheme thattakes into account constraints on the agent inputs and showthat it guarantees consensus under mild assumptions. Since theglobal cost does not decrease monotonically, it cannot be used asa Lyapunov function for proving consensus. Rather, our proofexploits geometric properties of the optimal path followed byindividual agents.