Consensus in Complex Networks with Noisy Agents and Peer Pressure

TL;DR

This paper analyzes a discrete-time consensus model in complex networks with noisy agents and peer pressure, demonstrating conditions for consensus and limitations on hidden state recovery, with empirical generalizations to complex graphs.

Contribution

It introduces a model with increasing peer-pressure and noise, proving consensus conditions and showing hidden states cannot be exactly recovered, with empirical insights on complex networks.

Findings

Consensus is achieved under certain peer-pressure conditions.

Hidden states cannot be exactly recovered despite known dynamics.

Results generalize empirically to complex graph structures.

Abstract

In this paper we study a discrete time consensus model on a connected graph with monotonically increasing peer-pressure and noise perturbed outputs masking a hidden state. We assume that each agent maintains a constant hidden state and a presents a dynamic output that is perturbed by random noise drawn from a mean-zero distribution. We show consensus is ensured in the limit as time goes to infinity under certain assumptions on the increasing peer-pressure term and also show that the hidden state cannot be exactly recovered even when model dynamics and outputs are known. The exact nature of the distribution is computed for a simple two vertex graph and results found are shown to generalize (empirically) to more complex graph structures.