Decentralized control for maintenance of strong connectivity for directed graphs

In order to accomplish cooperative tasks, decentralized systems are required to communicate among each other. Thus, maintaining the connectivity of the communication graph is a fundamental issue. Connectivity maintenance has been extensively studied in the last few years, but generally considering undirected communication graphs. In this paper we introduce a decentralized control and estimation strategy to maintain the strong connectivity property of directed communication graphs. The control strategy is initially developed for balanced digraphs, and is then extended to generic strongly connected digraphs, introducing a decentralized balancing algorithm. The control strategy is validated by means of analytical proofs and simulation results.