On the equivalence of model-based and data-driven approaches to the design of unknown-input observers
Giorgia Disarò, Maria Elena Valcher
TL;DR
This work addresses designing unknown-input observers (UIOs) for discrete-time LTI systems using only finite-window data, establishing necessary and sufficient data-driven solvability conditions that are equivalent to classical model-based criteria under a mild data Assumption. It provides a complete parametrization of all candidate UIOs through data-dependent matrices and proves a bijection between UIO descriptors and data-parameter matrices, enabling construction even when only historical data is available. A practical simplification recovers the state-space matrices by estimating $C$ from data and solving a reduced factorization to yield a Schur-stable $A_{UIO}$, with guidance from a cited algorithm, and a numerical example illustrates the equivalence and benefits of the data-driven approach. Overall, the paper shows that, with representative data, data-driven UIO design does not impose extra constraints beyond the model-based framework and offers a route to controller-observer synthesis when the system model is partially unknown.
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.