On the equivalence of model-based and data-driven approaches to the design of unknown-input observers

TL;DR

This paper demonstrates that data-driven methods for designing unknown-input observers for LTI systems are fundamentally equivalent to traditional model-based approaches, requiring no additional constraints under weak data assumptions.

Contribution

It establishes necessary and sufficient data-driven conditions for UIO design and proves their equivalence to classical model-based conditions for LTI systems.

Findings

Data-driven conditions match classical model-based conditions.

Weak data assumptions suffice for equivalence.

No additional constraints are imposed by data-driven approach.

Abstract

In this paper we investigate a data-driven approach to the design of an unknown-input observer (UIO). Specifically, we provide necessary and sufficient conditions for the existence of an unknown-input observer for a discrete-time linear time-invariant (LTI) system, designed based only on some available data, obtained on a finite time window. We also prove that, under weak assumptions on the collected data, the solvability conditions derived by means of the data-driven approach are in fact equivalent to those obtained through the model-based one. In other words, the data-driven conditions do not impose further constraints with respect to the classic model-based ones, expressed in terms of the original system matrices.