Data-Driven Reduced-Order Unknown-Input Observers
Giorgia Disarò, Maria Elena Valcher
TL;DR
The paper addresses state estimation for discrete-time LTI systems with unknown inputs by developing a data-driven design for reduced-order unknown-input observers (rUIOs). Building on model-based rUIO theory, it uses offline input/output/state trajectories to identify the output matrix and construct the observer directly from data, establishing necessary and sufficient conditions that are equivalent to the classical model-based criteria, including strong$^*$ detectability and Schur stability of the observer’s reduced-order dynamics $A_{UIO}$. The approach yields a data-driven acceptor of order $n-p$ with matrices $A_{UIO}, B_{UIO}^u, B_{UIO}^y, D_{UIO}$ expressible from data, and relies on a kernel inclusion $\ker(X_{f,1}) \supseteq \ker(U_pY_pY_fX_{p,1})$ for existence. A numerical example demonstrates successful, asymptotic convergence of the estimation error, illustrating practical benefits in reduced-complexity state estimation under unknown disturbances. The method promises efficient observer synthesis without full system identification, with potential impact on fault detection and robust estimation in data-rich settings.
Abstract
In this paper we propose a data-driven approach to the design of reduced-order unknown-input observers (rUIOs). We first recall the model-based solution, by assuming a problem set-up slightly different from those traditionally adopted in the literature, in order to be able to easily adapt it to the data-driven scenario. Necessary and sufficient conditions for the existence of a reduced-order unknown-input observer, whose matrices can be derived from a sufficiently rich set of collected historical data, are first derived and then proved to be equivalent to the ones obtained in the model-based framework. Finally, a numerical example is presented, to validate the effectiveness of the proposed scheme.