Spectral identification of networks with inputs

TL;DR

This paper extends spectral network identification methods to linear systems with external inputs, enabling the recovery of network properties from limited measurements, useful for network analysis and clustering.

Contribution

It introduces a novel approach to identify network eigenvalues in systems with inputs, reducing measurement requirements and enhancing applicability.

Findings

Successfully estimated mean, min, max node degree

Extended method to systems with external inputs

Demonstrated network clustering capabilities

Abstract

We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These eigenvalues allow to deduce some global properties of the network, such as bounds on the node degree. Having recently introduced this approach for autonomous networks of nonlinear systems, we extend it here to treat networked systems with external inputs on the nodes, in the case of linear dynamics. This is more natural in several applications, and removes the need to sometimes use several independent trajectories. We illustrate our framework with several examples, where we estimate the mean, minimum, and maximum node degree in the network. Inferring some information on the leading Laplacian eigenvectors, we also use our framework in the context of network clustering.