Distributed Stopping Criterion for Ratio Consensus

Distributed averaging of initial conditions held by multiple agents is a well-studied problem in context of networked systems where coordination amongst the agents is of paramount importance. The asymptotic nature of distributed averaging protocols makes it challenging to implement in practical settings as it does not lend itself to a finite-time stopping criterion that can be ascertained distributively. It is important that agents develop the ability to detect on their own when average of the initial conditions of the agents is achieved within some pre-specified tolerance and stop further computations. This article presents a distributed stopping criterion for distributed averaging using ratio consensus on a fixed interconnection topology (captured by a directed or undirected graph). The practical utility of the algorithm is illustrated through simulations.