G. Ferrari-Trecate, A. Buffa, and M. Gati. Analysis of coordination in multi-Agent systems through partial difference equations. IEEE Trans. on Automatic Control , 51(6):1058--1063, 2006.
In this paper we introduce the framework of Partial differenceEquations (PdEs) over graphs for analyzing the behavior of multi-agent systemsequipped with decentralized control schemes. Both leaderless andleader-follower models are considered. PdEsmimic Partial Differential Equations (PDEs) on graphs and can bestudied by introducing concepts of functional analysis strongly inspired tothe corresponding ones arising in PDEs theory. We generalize differentmodels proposed in the literature byintroducing errors in the agent dynamics and analyze agentcoordination through the joint use of PdEs andautomatic control tools. Moreover, for the simplest control schemes, weshow that the resulting PdEs enjoy properties that are similar tothose of well-known PDEslike the heat equation, thus allowing to exploit physical-based reasoningfor conjecturing formation properties.