Identifiability of Undirected Dynamical Networks: a Graph-Theoretic Approach

TL;DR

This paper introduces a graph-theoretic condition for the unique identifiability of undirected dynamical networks' state matrices, enabling network identification with minimal node excitation and measurement.

Contribution

It presents a novel graph coloring condition that guarantees identifiability and extends the framework to higher-order node dynamics.

Findings

Identifiability can be achieved without exciting or measuring all nodes.

The graph coloring condition provides a practical criterion for network identifiability.

Many network structures allow for successful identification with only small fractions of measured and excited nodes.

Abstract

This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state matrix of the network can be uniquely identified. As our main contribution, we present a graph coloring condition that ensures identifiability of the network's state matrix. Additionally, we show how the framework can be used to assess identifiability of dynamical networks with general, higher-order node dynamics. As an interesting corollary of our results, we find that excitation and measurement of all network nodes is not required. In fact, for many network structures, identification is possible with only small fractions of measured and excited nodes.