Decentralized Control of Connectivity for Multi-Agent Systems

In this paper we propose a decentralized algorithm to increase the connectivity of a multi-agent system. The connectivity property of the multi-agent system is quantified through the second smallest eigenvalue of the state dependent Laplacian of the proximity graph of agents. An exponential decay model is used to characterize the connection between agents. A supergradient algorithm is then used in conjunction with a recently developed decentralized algorithm for eigenvector computation to maximize the second smallest eigenvalue of the Laplacian of the proximity graph. A potential based control law is utilized to achieve the distances dictated by the supergradient algorithm. The algorithm is completely decentralized, where each agent receives information only from its neighbors, and uses this information to update its control law at each step of the iteration. Simulations demonstrate the effectiveness of the algorithm