Local Network Identifiability with Partial Excitation and Measurement

Abstract: This work focuses on the identifiability of dynamical networks with partial excitation and measurement: a set of nodes are interconnected by unknown transfer functions according to a known topology, some nodes are subject to external excitation, and some nodes are measured. The goal is to determine which transfer functions in the network can be recovered based on the input-output data collected from the excited and measured nodes. We propose a local version of network identifiability, representing the ability to recover transfer functions which are approximately known, or to recover them up to a discrete ambiguity. We show that local identifiability is a generic property, establish a necessary and sufficient condition in terms of matrix generic ranks, and exploit this condition to develop an algorithm determining, with probability 1, which transfer functions are locally identifiable. Our implementation presents the results graphically, and is publicly available.