On the Geometry of Consensus Algorithms with Application to Distributed Termination in Higher Dimension ?

摘要

We present insights into the geometry of the ratio consensus algorithm that lead to finite time distributed stopping criteria for the algorithm in higher dimension. In particular we show that the polytopes of network states indexed by time form a nested sequence. This monotonicity allows the construction of a distributed algorithm that terminates in finite time when applied to consensus problems in any dimension and guarantees the convergence of the consensus algorithm in norm, within any given tolerance. The practical utility of the algorithm is illustrated through MATLAB simulations.