Topological Conditions for Identifiability of Dynamical Networks with Partial Node Measurements

TL;DR

This paper establishes graph-theoretic conditions for the strong identifiability of dynamical networks with partial node measurements, introducing constrained vertex-disjoint paths to characterize network identifiability.

Contribution

It introduces a new graph-theoretic concept called constrained vertex-disjoint paths and provides conditions for strong identifiability of networks based on these paths.

Findings

Identifiability conditions are derived using constrained vertex-disjoint paths.

The approach applies to networks with known graph structures and partial measurements.

Results strengthen previous generic identifiability conditions by addressing all network matrices.

Abstract

This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in graph-theoretic conditions for identifiability of such dynamical networks, where we assume that only a subset of nodes is measured but the underlying graph structure of the network is known. This problem has recently been investigated in the case of generic identifiability. In this paper, we investigate a stronger notion of identifiability for all network matrices associated with a given graph. For this, we introduce a new graph-theoretic concept called constrained vertex-disjoint paths. As our main result, we state conditions for identifiability based on these constrained vertex-disjoint paths.