G. Ferrari-Trecate, L. Galbusera, M.P.E. Marciandi, and R. Scattolini. Model predictive control schemes for consensus in multi-Agent systems with integrator dynamics and time-varying communication. 3rd International Workshop on Networked Control Systems Tolerant to Faults (NECST07) , 2007. Nancy, France, 20-21 June.
In this paper we address the problem of driving a group of agents towardsa consensus point when agents have a discrete-time integrator dynamics andthe communication graph is time-varying. We propose two decentralized ModelPredictive Control (MPC) schemes that take into account constraints on theagents’ inputs and show that they guarantee consensus under mild assumptions.Since the global cost does not decrease monotonically, it cannot be used asa Lyapunov function for proving convergence to consensus. Rather, our proofsexploit geometric properties of the optimal path followed by individual agents.