Max-Consensus in a Max-Plus Algebraic Setting: The Case of Switching Communication Topologies

Abstract

Because of their use for distributed decision making, consensus algorithms have attracted a lot of interest in recent years. Coordination between entities requires that they share information over a network, and develop a consistent view regarding objectives and relevant information on the environment, i.e., reach a consensus. In practice, communication topologies may change over time, either as a consequence of disturbances or in an attempt to improve performance. Max-consensus is a specific consensus algorithm, which is particularly important in applications such as minimum time rendezvous and leader election. In this contribution, we propose an approach to analyze max-consensus algorithms in time-variant communication topologies, which is based on max-plus algebra. In this framework max-consensus algorithms become piecewise linear and may be analyzed easily. The conditions needed to achieve maxconsensus and the convergence rate of the algorithm for different communication graphs are studied. This contribution is an extension of the work in Monajemi Nejad et al. (2009), where max-consensus was studied for time-invariant communication topologies.

Analysis and Design of Robust Max Consensus for Wireless Sensor Networks

“…We consider a distributed network with N = 75 nodes, as shown in Figure 1. This irregular graph was randomly generated, which is commonly followed [9], [12], [13], [17].…”

“…Although max consensus has been studied in the literature [8]- [13], the analysis of max consensus algorithms Parts of this paper were presented at the 2018 Asilomar Conference on Signals, Systems and Computers [1]. G. Muniraju under additive channel noise and randomly changing network conditions has not received much attention.…”

“…Asynchronous updates in the presence of bounded delays is considered in [11]. Max-plus algebra is used to analyze convergence of max-consensus algorithms for timeinvariant communication topologies in [12], and for switching topologies in [13], both in the absence of noise. Distributed algorithms to reach consensus on general functions in the absence of noise are studied in [14]- [16].…”

“…A system model with imperfect transmissions is considered in [9], [13], where a message is received with a probability 1 − p. This model is equivalent to the time-varying graphs, where each edge is deleted independently with a probability p. However, these works do not consider errors in transmission, but only consider transmission failures (erasures).…”

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

“…An extension to time-variant (switching) communication topologies is reported elsewhere ( [19]). negotiating values of information states communication events Fig.…”