Identifiability of Undirected Dynamical Networks: A Graph-Theoretic Approach

This letter 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.

I. Introduction

Networks of dynamical systems appear in multiple contexts, including power networks, sensor networks, and robotic networks (see [1, Sec. 1]). It is natural to describe such networks by a graph, where nodes correspond with dynamical subsystems, and edges represent interaction between different systems. Often, the graph structure of dynamical networks is not directly available. For instance, in neuroscience, the interactions between brain areas are typically unknown [2]. Other examples of networks with unknown interconnection structure include genetic networks [3] and wireless sensor networks [4].