In this paper we address the problem of driving a group of agents towards a consensus point when agents have a discrete-time single-integrator dynamics and the communication graph is undirected and time-varying. We propose a decentralized Model Predictive Control (MPC) scheme that takes into account constraints on the agent inputs and show that it guarantees consensus under mild assumptions. Since the global cost does not decrease monotonically, it cannot be used as a Lyapunov function for proving consensus. Rather, our proof exploits geometric properties of the optimal path followed by individual agents.
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