G. Ferrari-Trecate, L. Galbusera, M.P.E. Marciandi, and R. Scattolini. Model predictive control schemes for consensus in multi-agent systems with single- and double-integrator dynamics. IEEE Trans. on Automatic Control , 54(11):2560--2572, 2009.
In this paper we address the problem of driving a groupof agents towards a consensus point when the agents have adiscrete-time single- or double-integrator dynamics and thecommunication network is time-varying. We propose decentralizedModel Predictive Control (MPC) schemes that take into accountconstraints on the agents' input and show that they guaranteeconsensus under mild assumptions. Since the global cost does notdecrease monotonically, it cannot be used as a Lyapunov functionfor proving convergence to consensus. For this reason, our proofsexploit geometric properties of the optimal path followed byindividual agents.