Identifiability and Maximum Likelihood Estimation for System Identification of Networks of Dynamical Systems

TL;DR

This work addresses identifiability and maximum likelihood estimation for direct identification in networks of dynamical systems. It introduces a Gröbner-basis framework to characterize network identifiability and develops ML estimators that are consistent and efficient, contrasting with PEM approaches. To tackle numerical challenges, it derives a predictor-free ML formulation and an equivalent unconstrained optimization, enabling practical computation. Numerical experiments show the ML method matches PEM when applicable and remains effective when PEM fails, highlighting its applicability under network identifiability regardless of PEM suitability.

Abstract

In this paper we investigate identifiability and maximum likelihood estimation for direct system identification of networks of dynamical systems. We provide necessary and sufficient conditions for network identifiability in terms of Gröbner bases. We show that the maximum likelihood approach is both consistent and efficient, which is in contrast to existing prediction error approaches. Moreover, our approach has wider applicability, i.e., it is applicable whenever network identifiability holds. Finally, we show that we can formulate the maximum likelihood problem without the use of a predictor, which is the key to numerically being able to solve it efficiently.

Figures (1)

• Figure 1: Block diagram for a dynamic network where $\mathbf{v}^i =\mathbf{H}^i\mathbf{e}^i$.

Theorems & Definitions (26)

• Lemma 1
• Remark 1
• Theorem 2
• Remark 2
• Lemma 3
• Theorem 4
• Corollary 4.1
• Remark 3
• Lemma 5
• Lemma 6