G. Ferrari-Trecate, A. Buffa, and M. Gati. Analysis of coordination in multi-agent systems through partial difference equations. part ii: Nonlinear control. 16th IFAC World Congress on Automatic Control , 2005. Prague, Czech Republic, 3-8 July.
In this second part of the paper we exploit the framework of Partial differenceEquations (PdEs) over graphs for analyzing the behavior of multi-agent systems equipped with potential field based control schemes. We consider agent dynamics affected by errors and model the collective dynamicsthrough nonlinear PdEs. Hinging on theproperties of the Laplacian operator on graph, discussed in Part I, we prove alignment and collision avoidance both in leaderless and leader-followermodels.