Nonlinear network identifiability: The static case

TL;DR

This paper investigates the conditions under which nonlinear network structures can be uniquely identified from static measurements, focusing on different classes of functions and graph topologies.

Contribution

It provides new identifiability conditions for nonlinear network models, including paths, trees, and directed acyclic graphs, under various function classes.

Findings

Identifiability requires measuring all nodes except the source in general nonlinear cases.

For analytic functions with $f(0)=0$, conditions for paths and trees are established.

For nonlinear functions excluding linear ones, conditions for directed acyclic graphs are derived.

Abstract

We analyze the problem of network identifiability with nonlinear functions associated with the edges. We consider a static model for the output of each node and by assuming a perfect identification of the function associated with the measurement of a node, we provide conditions for the identifiability of the edges in a specific class of functions. First, we analyze the identifiability conditions in the class of all nonlinear functions and show that even for a path graph, it is necessary to measure all the nodes except by the source. Then, we consider analytic functions satisfying $f(0)=0$ and we provide conditions for the identifiability of paths and trees. Finally, by restricting the problem to a smaller class of functions where none of the functions is linear, we derive conditions for the identifiability of directed acyclic graphs. Some examples are presented to illustrate the results.