G. Ferrari-Trecate, A. Buffa, and M. Gati. Analysis of coordination in multi-agent systems through partial difference equations. part i: The laplacian control. 16th IFAC World Congress on Automatic Control , 2005. Prague, Czech Republic, 3-8 July.
In this first part of a two-parts paper we introduce the framework of Partial differenceEquations (PdEs) over graphs for analyzing the behavior of multi-agent systems equipped with decentralized control schemes. We generalize theVicsek's model byintroducing errors in the agent dynamics and analyze agentalignment in leaderless and leader-follower models through the joint use of PdEs andautomatic control tools. Moreover, weshow that the resulting PdEs enjoy properties that are similar tothose of well-known Partial Differential Equations (PDEs)like the heat equation, thus allowing to exploit physical-based reasoningfor conjecturing properties of the collective dynamics.