ADMM for Dynamic Average Consensus over Imperfect Networks
Nicola Bastianello, Ruggero Carli
Abstract
In this paper we propose and analyze a distributed algorithm for dynamic average consensus that is derived in the context of online optimization and based on the alternating direction method of multipliers (ADMM). In particular, we are interested in a scenario in which the multi-agent system is subject to the following challenges: (i) asynchronous activation of the nodes, (ii) peer-to-peer communication failures, (iii) random additive noise on the communications. We provide theoretical results that characterize the mean linear convergence of the algorithm's output within a neighborhood of the average consensus, and bound the radius of this neighborhood. We discuss the results highlighting the contributions of different factors (network, speed of the consensus variation, ...), and present numerical results that compare the proposed algorithm with alternative methods.