Analysis of coordination in multi-agent systems through partial difference equations. Part II: Nonlinear control

In this second part of the paper we exploit the framework of Partial difference Equations (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 dynamics through nonlinear PdEs. Hinging on the properties of the Laplacian operator on graph, discussed in Part I, we prove alignment and collision avoidance both in leaderless and leader-follower models.