Non-Linear Distributed Average Consensus using Bounded Transmissions

TL;DR

This paper introduces a distributed average consensus algorithm with bounded power transmissions, analyzing its asymptotic behavior and convergence properties in noisy communication environments.

Contribution

It proposes a novel non-linear consensus algorithm that ensures bounded transmissions and characterizes its asymptotic performance using stochastic approximation theory.

Findings

Nodes reach consensus asymptotically to a finite random variable

Bounded transmissions lead to slower convergence than linear algorithms

Simulations validate the analytical results

Abstract

A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable whose expectation is the desired sample average of the initial observations with a variance that depends on the step size of the algorithm and the variance of the communication noise. The asymptotic performance is characterized by deriving the asymptotic covariance matrix using results from stochastic approximation theory. It is shown that using bounded transmissions results in slower convergence compared to the linear consensus algorithm based on the Laplacian heuristic. Simulations corroborate our analytical findings.