Path-Based Conditions for Local Network Identifiability -- Full Version

TL;DR

This paper investigates conditions under which unknown transfer functions in a dynamical network can be generically identified from input-output data, introducing a decoupled identifiability concept linked to graph path conditions.

Contribution

It introduces a decoupled generic identifiability framework and establishes necessary and sufficient graph-theoretic conditions for local network identifiability.

Findings

Necessary condition based on vertex-disjoint paths in an augmented graph.

Sufficient condition for decoupled identifiability.

Proposes a new perspective linking network identifiability to graph path properties.

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 propose a decoupled version of generic identifiability that is necessary for generic local identifiability and might be equivalent as no counter-example to sufficiency has been found yet in systematic trials. This new notion can be interpreted as the generic identifiability of a larger network, obtained by duplicating the graph, exciting one copy and measuring the other copy. We establish a necessary condition for decoupled identifiability in terms of vertex-disjoint paths in the larger graph, and a sufficient one.