Stable motion and distributed topology control for multi-agent systems with directed interactions

In this paper, we study stable coordination in multiagent systems with directed interactions, and apply the results for distributed topology control. Our main contribution is to extend the well-known potential-based control framework originally introduced for undirected networks to the case of networks modeled by a directed graph. Regardless of the particular objective to be achieved, potential-based control for undirected graphs is intrinsically stable. Briefly, this can be explained by the positive semidefiniteness of the graph Laplacian induced by the symmetric nature of the interactions. Unfortunately, this energy finiteness guarantee no longer holds when a multi-agent system lacks symmetry in pairwise interactions. In this context, our contribution is twofold: i) we formalize stable coordination of multi-agent systems on directed graphs, demonstrating the graph structures that induce stability for a broad class of coordination objectives; and ii) we design a topology control mechanism based on a distributed eigenvalue estimation algorithm to enforce Lyapunov energy finiteness over the derived class of stable graphs. Simulation results demonstrate a multi-agent system on a directed graph performing topology control and collision avoidance, corroborating the theoretical findings.