Model Predictive Control Schemes for Consensus in Multi-Agent Systems with Single- and Double-Integrator Dynamics

In this paper, we address the problem of driving a group of agents towards a consensus point when the agents have a discrete-time single- or double-integrator dynamics and the communication network is time-varying. We propose decentralized model predictive control schemes that take into account constraints on the agents´ input and show that they guarantee consensus under mild assumptions. Since the global cost does not decrease monotonically, it cannot be used as a Lyapunov function for proving convergence to consensus. For this reason, our proofs exploit geometric properties of the optimal path followed by individual agents.