Combinatorial Characterization for Global Identifiability of Separable Networks with Partial Excitation and Measurement

TL;DR

This paper provides a combinatorial framework to determine the global identifiability of separable dynamical networks with partial excitation and measurement, enabling recovery of unknown transfer functions from input-output data.

Contribution

It introduces the concept of separable networks and offers a necessary and sufficient combinatorial characterization for their local identifiability, applicable to general network topologies.

Findings

A necessary and sufficient condition for local identifiability based on path existence and parity.

Separable networks have equivalent global and local identifiability.

A necessary condition for identifiability applicable to all network types.

Abstract

This work focuses on the generic identifiability of dynamical networks with partial excitation and measurement: a set of nodes are interconnected by transfer functions according to a known topology, some nodes are excited, some are measured, and only a part of the transfer functions are known. Our goal is to determine whether the unknown transfer functions can be generically recovered based on the input-output data collected from the excited and measured nodes. We introduce the notion of separable networks, for which global and so-called local identifiability are equivalent. A novel approach yields a necessary and sufficient combinatorial characterization for local identifiability for such graphs, in terms of existence of paths and conditions on their parity. Furthermore, this yields a necessary condition not only for separable networks, but for networks of any topology.