Distributed Average Consensus Over Noisy Communication Links in Directed Graphs

Motivated by the needs of resiliency, scalability, and plug-and-play operation, distributed decision-making is becoming increasingly prevalent. The problem of achieving consensus in a multi-agent system is at the core of distributed decision-making. In this article, we study the problem of achieving average consensus over a directed multi-agent network when the communication links are corrupted with noise. We propose an algorithm where each agent updates its estimates based on the local mixing of information and adds its weighted noise-free initial information to its updates during every iteration. We demonstrate that with appropriately designed weights the agents achieve consensus under additive communication noise. We establish that when the communication links are noiseless the proposed algorithm moves towards consensus at a geometric rate. Under communication noise, we prove that the agent estimates reach a consensus value almost surely. We present numerical experiments to corroborate the efficacy of the proposed algorithm under different noise realizations and various algorithm parameters.