# Willems' fundamental lemma for linear descriptor systems and its use for data-driven output-feedback MPC

arXiv: https://arxiv.org/abs/2202.07930 · HTML: https://mlsanity.com/paper/2202.07930/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2022.

## Built on by (most cited first, 1 of 1)

- [Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study](https://mlsanity.com/paper/2401.04508/) (2024)

## Abstract (arXiv)

In this paper we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems' fundamental lemma, which shows that for descriptor systems the non-parametric modelling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constraints. Moreover, we use this description to propose a data-driven framework for optimal control and predictive control of discrete-time linear descriptor systems. For the latter, we provide a sufficient stability condition for receding-horizon control before we illustrate our findings with an example.