G. Ferrari-Trecate, A. Buffa, and M. Gati. Analysis of coordination in multiple agents formations through partial difference equations. Technical Report N.5-PV, Istituto di Matematica Applicata e Tecnologie Informatiche, C.N.R., Pavia, Italy, 2004.
In this paper we introduce the framework of Partial differenceEquations (PdEs) over graphs for analyzing the behavior of multipleagent formations equipped with decentralized control schemes. PdEsmimic Partial Differential Equations (PDEs) on graphs and can bestudied by introducing functional analysis concepts strongly inspired tothe corresponding ones arising in PDEs theory. We generalize differentformation models 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.