A Decentralized Asymmetric Weighting Approach for Improved Convergence of Multi-Agent Systems with Directed Interaction

This work considers the convergence rate of multi-agent systems with discrete-time single-integrator dynamics and undirected interaction topologies. In recent work it has been proven that in case of lattice interaction topologies the convergence rate can be bounded away from zero, independent of the network size, using asymmetric weightings that give the interaction graph a preferred communication direction. Approximation methods for more general graphs, based on relative angles between agents, are presented, which suggest that the convergence rate is bounded away from zero as well. This work proposes alternative approximation methods, that improve the convergence rate compared to previous approximation methods. Furthermore it is shown that the improvement of the approximation methods degrade in comparison to other weighting approaches, the more the considered topology differs from a lattice graph. Therefore an iterative algorithm is proposed, that extends the idea of a preferred communication direction to general graphs, which are not similar to lattices or where the relative angles are not known.