Control schemes based on the wave equation for consensus in multi-agent systems with double-integrator dynamics

Abstract

In this paper, we consider the problem of driving a group of agents communicating through an undirected and weighted network towards a consensus point. We assume that agents obey to double-integrator dynamics and study decentralized control schemes for consensus of the position variables. In particular we revisit control policies proposed in [1] and [2] in the unified framework of Partial difference Equations over graphs and highlight the link between the closed-loop system dynamics and the damped wave equation describing the motion of a free elastic beam.