Max-consensus in a max-plus algebraic setting: The case of fixed communication topologies

Consensus algorithms have been studied in the field of distributed computing for decades. Recently consensus algorithms have attracted renewed attention because they can be exploited for distributed cooperative control. The purpose of this paper is the analysis of a specific class of consensus algorithms called max-consensus. This class of algorithms is needed for applications such as minimum time rendezvous and leader election. A new approach using max-plus algebra is proposed to analyze convergence of max-consensus algorithm. In this paper we focus on the problem of achieving max-consensus in time-invariant communication topologies. Conditions to achieve max-consensus are discussed and the convergence rate of the algorithm for different communication topologies is studied.