Network Reconstruction in Consensus Algorithms with Hidden Agents

TL;DR

This paper introduces a method to reconstruct the influence network in leader-follower consensus systems with hidden leaders, using autoregressive expansion and numerical simulations.

Contribution

It provides a novel approach to reconstruct network parameters in systems with hidden agents, leveraging directed Laplacian coupling and autoregressive models.

Findings

Successfully reconstructs the full dynamical matrix with hidden leaders

Applicable when leaders have short memory and certain assumptions are met

Validated through numerical simulations with single and multiple hidden leaders

Abstract

Reconstructing the parameters that encode the influence between model variables based on time-series measurements represents an outstanding question in the theory of complex network-coupled systems. Here, we propose a solution to this problem for a class of noisy leader-follower consensus algorithm, where one has access to measurements only from the followers but not from the leaders. Leveraging the directed Laplacian coupling of such systems, we present an autoregressive expansion of the observed dynamics which can be truncated at different orders, depending on the memory of the leaders. When their memory is short, this allows one to correctly reconstruct the full dynamical matrix with hidden leader agents, provided some additional assumption on the system to lift the degeneracy in the reconstruction. We illustrate and check the theory using numerical simulations for the cases of both a single and multiple hidden leaders.