Utilizing Feedback Channel Mechanisms for Reaching Average Consensus over Directed Network Topologies

In this paper, we address the problem of discretetime average consensus, where agents (nodes) exchange information over unreliable communication links. We enhance the Robustified Ratio Consensus algorithm by embedding the Automatic Repeat ReQuest (ARQ) protocol used for error control of data transmissions, in order to allow the agents to reach asymptotic average consensus while handling time-varying delays induced by retransmissions of erroneous packets, and possible packet drops that occur due to excess of a predefined packet retransmission limit imposed by the ARQ protocol. Invoking the ARQ protocol allows nodes to: (a) exploit the incoming error-free acknowledgement feedback signals to initially acquire or later update their out-degree, (b) know whether a packet has arrived or not, and (c) determine a local upper-bound on the delays which is imposed by the retransmission limit. The analysis of our proposed algorithm, herein called the ARQ-based Ratio Consensus algorithm, relies on augmenting the network’s corresponding weighted adjacency matrix, to handle time-varying (yet bounded) delays and possible packet drops. To the best of the authors’ knowledge, this is the first consensus algorithm that incorporates a communication protocol for error control used in real communication systems with feedback.