Fiedler-Based Characterization and Identification of Leaders in Semi-Autonomous Networks

TL;DR

This paper presents a spectral and data-driven method to identify leader nodes in semi-autonomous consensus networks using steady-state velocity data and Fiedler vector properties, without needing network topology.

Contribution

It introduces a novel approach combining spectral graph theory and relative tempo measurements to detect leaders solely from agent velocities.

Findings

Successfully reconstructs Fiedler vector from velocity data

Identifies leader nodes without prior network topology knowledge

Validated through numerical simulations demonstrating effectiveness

Abstract

This paper addresses the problem of identifying leader nodes in semi-autonomous consensus networks from observed agent dynamics. Using the grounded Laplacian formulation, we derive spectral conditions that ensure the components of the Fiedler vector associated with leader and follower nodes are distinct. Building on the foundation, we emply the notion of relative tempo from prio works as an observable quantity that relates agents' steady-state velocities to the Fiedler vector. This relationship enables the development of a data-driven algorithm that reconstructs the Fiedler vector - and consequently identifies the leader set - using only steady-state velocity measurements, without requiring knowledge of the network topology. The proposed approach is validated through nuerical examples, demonstrating how spectral properties and relative tempo measurements can be combined to reveal hidden leadership structures in consensus networks.