Ferrari-Trecate, G.Buffa, A.Gati, M.2017-01-102017-01-102017-01-10200510.3182/20050703-6-CZ-1902.02086https://infoscience.epfl.ch/handle/20.500.14299/132657In this first part of a two-parts paper we introduce the framework of Partial difference Equations (PdEs) over graphs for analyzing the behavior of multi-agent systems equipped with decentralized control schemes. We generalize the Vicsek's model by introducing errors in the agent dynamics and analyze agent alignment in leaderless and leader-follower models through the joint use of PdEs and automatic control tools. Moreover, we show that the resulting PdEs enjoy properties that are similar to those of well-known Partial Differential Equations (PDEs) like the heat equation, thus allowing to exploit physical-based reasoning for conjecturing properties of the collective dynamics.text::conference output::conference proceedings::conference paper