Analysis and Design of Robust Max Consensus for Wireless Sensor Networks

Abstract

A novel distributed algorithm for estimating the maximum of the node initial state values in a network, in the presence of additive communication noise is proposed. Conventionally, the maximum is estimated locally at each node by updating the node state value with the largest received measurements in every iteration. However, due to the additive channel noise, the estimate of the maximum at each node drifts at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used as a tool to study this ergodic process. The subadditive ergodic theorem is invoked to establish a constant growth rate for the state values due to noise, which is studied by analyzing the max-plus Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is upper bounded by a constant which depends on the spectral radius of the network and the noise variance. Upper and lower bounds are derived for both fixed and random graphs. Finally, a two-run algorithm robust to additive noise in the network is proposed and its variance is analyzed using concentration inequalities. Simulation results supporting the theory are also presented.Index Terms-Max consensus, spectral radius, max-plus algebra, wireless sensor networks.

Dynamic Min and Max Consensus and Size Estimation of Anonymous Multiagent Networks

“…The popular protocol which solves the (static) maxconsensus problem [18], [26], [27], [34] makes use of the following local interaction rule,…”

“…Asynchronous updates and communications affected by time-delays have been considered in [18], while a stochastic framework for asynchronous updates has been proposed in [21]. The effect of noise in communications among the agents has been characterized in [26], [39]. Finally, in the context of open multi-agent systems where the size and composition of the network is time-varying, a gossip algorithm has been proposed in [1].…”

Distributed Mechanism for Detecting Average Consensus with Maximum-Degree Weights in Bipartite Regular Graphs

“…Therefore, the application of a distributed consensus algorithm ensures that the sensor nodes can easily exchange local information about the observed quantity, update their local observations, and eventually obtain a precise estimate (or even the exact value) about the global status of the observed physical quantity in WSNs [22]. Thus, as found in the literature [35][36][37], distributed consensus algorithms for data aggregation have been becoming a fundamental complement in many WSNs over the past years.…”

Consensus based Data Transfer in Wireless Sensor Network for Reliability Interpretation

“…Spectral radius of a network with its upper bound upon growth rate including noise coefficients and failed transmissions has been discussed [2]. However, sensor nodes collision in transmissions is inevitable in upper bounds of growth rates which drift the actual calculations used.…”