Informativity and Identifiability for Identification of Networks of Dynamical Systems

TL;DR

This paper introduces a method using Gr"obner bases to analyze the informativity and identifiability of dynamical system networks, providing conditions based on spectral properties and transfer function ranks.

Contribution

It offers a novel algebraic approach to assess network identifiability and informativity through spectral analysis and transfer function dimension computation.

Findings

Spectral positive definiteness ensures informativity.

Full generic rank of transfer functions indicates network identifiability.

Method enables algebraic verification of network properties.

Abstract

In this paper, we show how informativity and identifiability for networks of dynamical systems can be investigated using Gr\"obner bases. We provide a sufficient condition for informativity in terms of positive definiteness of the spectrum of external signals and full generic rank of the transfer function relating the external signals to the inputs of the predictor. Moreover, we show how generic local network identifiability can be investigated by computing the dimension of the fiber associated with the closed loop transfer function from external measurable signals to the measured outputs.