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Informativity and Identifiability for Identification of Networks of Dynamical Systems

Anders Hansson, João Victor Galvão da Mata, Martin S. Andersen

TL;DR

This paper provides 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.

Abstract

In this paper, we show how informativity and identifiability for networks of dynamical systems can be investigated using Gröbner 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.

Informativity and Identifiability for Identification of Networks of Dynamical Systems

TL;DR

This paper provides 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.

Abstract

In this paper, we show how informativity and identifiability for networks of dynamical systems can be investigated using Gröbner 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.
Paper Structure (11 sections, 4 theorems, 48 equations, 1 figure)

This paper contains 11 sections, 4 theorems, 48 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Model of Network
  3. Innovation form and Predictor
  4. Informativity
  5. Graphical Condition
  6. Gröbner Basis Condition
  7. Identifiability
  8. Sub-Networks
  9. Example
  10. Numerical Examples
  11. Conclusions

Key Result

Theorem 1

Assume that the spectrum of $u_k=(r_k,e_k)$ is positive definite and that the generic rank of $\Pi$ is full, then $z_k$ is informative enough.

Figures (1)

  • Figure 1: Block diagram for a simple network.

Theorems & Definitions (23)

  • Definition 1
  • Theorem 1
  • Remark 1
  • Theorem 2
  • Remark 2
  • Remark 3
  • Theorem 3
  • Remark 4
  • Remark 5
  • Remark 6
  • ...and 13 more