Nonlinear Network Identifiability with Full Excitations

TL;DR

This paper establishes conditions for identifying nonlinear network structures with full node excitation, highlighting the importance of sink measurements and the impact of constant terms and cycles on identifiability.

Contribution

It provides new theoretical conditions for nonlinear network identifiability, extending previous linear results to more complex nonlinear and cyclic networks.

Findings

Measurement of all sinks is necessary and sufficient for acyclic graphs without constant terms.

Presence of constant terms prevents identifiability if a node has multiple in-neighbors.

For cyclic graphs, measuring one sink per sink in the condensation graph suffices.

Abstract

We derive conditions for the identifiability of nonlinear networks characterized by additive dynamics at the level of the edges when all the nodes are excited. In contrast to linear systems, we show that the measurement of all sinks is necessary and sufficient for the identifiability of directed acyclic graphs, under the assumption that dynamics are described by analytic functions without constant terms (i.e., $f(0)=0$). But if constant terms are present, then the identifiability is impossible as soon as one node has more than one in-neighbor. In the case of general digraphs that may contain cycles, we consider additively separable functions for the analysis of the identifiability, and we show that the measurement of one node of all the sinks of the condensation digraph is necessary and sufficient. Several examples are added to illustrate the results.