Consensus in complex networks with noisy agents and peer pressure

• Published in: Physica A 2022-12, Vol.608, p.128263, Article 128263
• Main Authors: Griffin, Christopher, Squicciarini, Anna, Jia, Feiran
• Format: Article
• Language: English
• Subjects: Consensus; Hidden state recovery; Noise; Peer-pressure; Privacy
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2022.128263

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. •Consensus on connected graphs with hidden states and noisy agents is formulated.•Sufficient criteria for convergence to consensus is provided.•Theoretical characterization of statistics on recovered hidden states provided.•Experimental results validate statistical analysis.