A behavioral approach for LPV data-driven representations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912671257853952 |
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| author | Verhoek, Chris Markovsky, Ivan Haesaert, Sofie Tóth, Roland |
| author_facet | Verhoek, Chris Markovsky, Ivan Haesaert, Sofie Tóth, Roland |
| contents | In this paper, we present a data-driven representation for linear parameter-varying (LPV) systems, which can be used for direct data-driven analysis and control of such systems. Specifically, we use the behavioral approach to develop a data-driven representation of the finite-horizon behavior of LPV systems for which there exists a kernel representation with shifted-affine scheduling dependence. Moreover, we provide a necessary and sufficient rank-based test on the available data that concludes whether the data fully represents the finite-horizon LPV behavior. Using the proposed data-driven representation, we also solve the data-driven simulation problem for LPV systems. Through multiple examples, we demonstrate that the results in this paper allow us to formulate a novel set of direct data-driven analysis and control methods for LPV systems, which are also applicable for LPV embeddings of nonlinear systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18543 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A behavioral approach for LPV data-driven representations Verhoek, Chris Markovsky, Ivan Haesaert, Sofie Tóth, Roland Systems and Control Optimization and Control In this paper, we present a data-driven representation for linear parameter-varying (LPV) systems, which can be used for direct data-driven analysis and control of such systems. Specifically, we use the behavioral approach to develop a data-driven representation of the finite-horizon behavior of LPV systems for which there exists a kernel representation with shifted-affine scheduling dependence. Moreover, we provide a necessary and sufficient rank-based test on the available data that concludes whether the data fully represents the finite-horizon LPV behavior. Using the proposed data-driven representation, we also solve the data-driven simulation problem for LPV systems. Through multiple examples, we demonstrate that the results in this paper allow us to formulate a novel set of direct data-driven analysis and control methods for LPV systems, which are also applicable for LPV embeddings of nonlinear systems. |
| title | A behavioral approach for LPV data-driven representations |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2412.18543 |