From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912883327107072 |
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| author | Meijer, T. J. Scheres, K. J. A. Nouwens, S. A. N. Dolk, V. S. Heemels, W. P. M. H. |
| author_facet | Meijer, T. J. Scheres, K. J. A. Nouwens, S. A. N. Dolk, V. S. Heemels, W. P. M. H. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_19390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control Meijer, T. J. Scheres, K. J. A. Nouwens, S. A. N. Dolk, V. S. Heemels, W. P. M. H. Optimization and Control Systems and Control 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. |
| title | From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2501.19390 |