Multiagent Consensus With Noisy Communication: Stopping Rules Based on Network Graphs

A stopping rule is presented for a multiagent consensus algorithm with noisy communication. A stochastic approximation method is employed and the relation between the closeness of the agreement and the number of iterations is established. A bound of the variation of the agents at the specific number of iterations is then derived with a probabilistic guarantee, which gives a rigorous stopping rule of the consensus algorithm with noisy communication. This stopping rule is given in terms of characteristic values of communication network graphs, which suggests a difference in transient behaviors by undirected and directed graphs. These theoretical results are demonstrated through numerical examples.