A Necessary Condition for Network Identifiability with Partial Excitation and Measurement

TL;DR

This paper establishes a necessary condition for identifying the dynamics of a network with partial excitation and measurement, using graph-based analysis, and provides a complete criterion for circular networks.

Contribution

It introduces a new necessary condition for network identifiability with partial measurements and excitations, and characterizes it via an edge-removal graph procedure.

Findings

A necessary condition for network identifiability is derived.

The condition is characterized using an edge-removal procedure on bipartite graphs.

A necessary and sufficient condition is provided for circular networks.

Abstract

This paper considers dynamic networks where vertices and edges represent manifest signals and causal dependencies among the signals, respectively. We address the problem of how to determine if the dynamics of a network can be identified when only partial vertices are measured and excited. A necessary condition for network identifiability is presented, where the analysis is performed based on identifying the dependency of a set of rational functions from excited vertices to measured ones. This condition is further characterised by using an edge-removal procedure on the associated bipartite graph. Moreover, on the basis of necessity analysis, we provide a necessary and sufficient condition for identifiability in circular networks.