From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control
Abstract
Willems' fundamental lemma has recently received an impressive amount of attention from the data-driven control community. In this paper, we formulate a version of this celebrated result based on frequency-domain data. In doing so, we bridge the gap between recent developments in data-driven control, and the readily-available techniques and expertise for non-parametric frequency-domain identification. We also generalize our results to combine multiple frequency-domain data sets to form a sufficiently rich data set. Building on these results, we propose a data-driven predictive control scheme based on measured frequency-domain data of the plant. This novel scheme provides a frequency-domain counterpart of the well-known data-enabled predictive control scheme DeePC based on time-domain data. Under appropriate conditions, the new frequency-domain data-driven predictive control (FreePC) scheme is equivalent to the corresponding DeePC scheme. We demonstrate the benefits of FreePC and the use of frequency-domain data in several examples and a numerical case study, including the ability to collect data in closed loop, computational benefits, and intuitive visualization of the data.
Keywords
Cite
@article{arxiv.2501.19390,
title = {From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control},
author = {T. J. Meijer and K. J. A. Scheres and S. A. N. Nouwens and V. S. Dolk and W. P. M. H. Heemels},
journal= {arXiv preprint arXiv:2501.19390},
year = {2026}
}