Local Network Identifiability with Partial Excitation and Measurement

TL;DR

This paper investigates the conditions under which transfer functions in a partially excited and measured dynamical network can be locally identified, providing a generic rank-based criterion and an algorithm for practical determination.

Contribution

It introduces a local identifiability concept for dynamical networks, establishes a rank-based necessary and sufficient condition, and develops an algorithm for identifying recoverable transfer functions.

Findings

Local identifiability is a generic property.

A rank-based criterion determines which transfer functions are identifiable.

An algorithm with probabilistic guarantees identifies locally recoverable transfer functions.

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.