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arXiv · 2501.19390

From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control

T. J. Meijer·K. J. A. Scheres·S. A. N. Nouwens·V. S. Dolk·W. P. M. H. Heemels
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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.

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T. J. Meijer, K. J. A. Scheres, S. A. N. Nouwens, V. S. Dolk, W. P. M. H. Heemels. 2025-01-31. From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control. https://arxiv.org/abs/2501.19390

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