REACHING A CONSENSUS IN A DYNAMICALLY CHANGINGENVIRONMENT: CONVERGENCE RATES, MEASUREMENTDELAYS, AND ASYNCHRONOUS EVENTS

摘要

This paper uses recently established properties of compositions of directed graphstogether with results from the theory of nonhomogeneous Markov chains to derive worst case conver-gence rates for the headings of a group of mobile autonomous agents which arise in connection withthe widely studied Vicsek consensus problem. The paper also uses graph-theoretic constructions tosolve modified versions of the Vicsek problem in which there are measurement delays, asynchronousevents, or a group leader. In all three cases the conditions under which consensus is achieved proveto be almost the same as the conditions under which consensus is achieved in the synchronous,delay-free, leaderless case.