Distributed Design of Finite-time Average Consensus Protocols

International audience; In this paper, we are interested in the finite-time average consensus problem for multi-agent systems or wireless sensor networks. This issue is formulated in a discrete-time framework by utilizing a linear iteration scheme, where each node repeatedly updates its value as a weighted linear combination of its own value and those of its neighbors. Unlike most of research in literature, this work deals with the foremost step, called configuration step, during which the consensus protocol is to be set up in each agent. Designing consensus protocols can be viewed as a matrix factorization problem. For connected undirected graphs, we propose a learning method for solving such matrix factorization problem in a distributed way.More precisely,we first show how solving this problemfor the particular case of strongly regular graphs. Then, a distributed gradient back-propagation algorithm is derived for the general case. The performance of the proposed algorithm is evaluated by means of simulation results.