1Model Predictive Control Schemes for Consensus in Multi-Agent Systems with Single- and Double-Integrator Dynamics

Abstract—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 decen-tralized Model Predictive Control (MPC) 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. Index Terms—Networked autonomous agents, Consensus prob-lems, Decentralized model predictive control. I