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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2311.03197 |
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| _version_ | 1866929289180479488 |
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| author | Di Natale, Loris Zakwan, Muhammad Svetozarevic, Bratislav Heer, Philipp Ferrari-Trecate, Giancarlo Jones, Colin N. |
| author_facet | Di Natale, Loris Zakwan, Muhammad Svetozarevic, Bratislav Heer, Philipp Ferrari-Trecate, Giancarlo Jones, Colin N. |
| contents | Machine Learning (ML) and linear System Identification (SI) have been historically developed independently. In this paper, we leverage well-established ML tools - especially the automatic differentiation framework - to introduce SIMBa, a family of discrete linear multi-step-ahead state-space SI methods using backpropagation. SIMBa relies on a novel Linear-Matrix-Inequality-based free parametrization of Schur matrices to ensure the stability of the identified model.
We show how SIMBa generally outperforms traditional linear state-space SI methods, and sometimes significantly, although at the price of a higher computational burden. This performance gap is particularly remarkable compared to other SI methods with stability guarantees, where the gain is frequently above 25% in our investigations, hinting at SIMBa's ability to simultaneously achieve state-of-the-art fitting performance and enforce stability. Interestingly, these observations hold for a wide variety of input-output systems and on both simulated and real-world data, showcasing the flexibility of the proposed approach. We postulate that this new SI paradigm presents a great extension potential to identify structured nonlinear models from data, and we hence open-source SIMBa on https://github.com/Cemempamoi/simba. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03197 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stable Linear Subspace Identification: A Machine Learning Approach Di Natale, Loris Zakwan, Muhammad Svetozarevic, Bratislav Heer, Philipp Ferrari-Trecate, Giancarlo Jones, Colin N. Systems and Control Machine Learning Machine Learning (ML) and linear System Identification (SI) have been historically developed independently. In this paper, we leverage well-established ML tools - especially the automatic differentiation framework - to introduce SIMBa, a family of discrete linear multi-step-ahead state-space SI methods using backpropagation. SIMBa relies on a novel Linear-Matrix-Inequality-based free parametrization of Schur matrices to ensure the stability of the identified model. We show how SIMBa generally outperforms traditional linear state-space SI methods, and sometimes significantly, although at the price of a higher computational burden. This performance gap is particularly remarkable compared to other SI methods with stability guarantees, where the gain is frequently above 25% in our investigations, hinting at SIMBa's ability to simultaneously achieve state-of-the-art fitting performance and enforce stability. Interestingly, these observations hold for a wide variety of input-output systems and on both simulated and real-world data, showcasing the flexibility of the proposed approach. We postulate that this new SI paradigm presents a great extension potential to identify structured nonlinear models from data, and we hence open-source SIMBa on https://github.com/Cemempamoi/simba. |
| title | Stable Linear Subspace Identification: A Machine Learning Approach |
| topic | Systems and Control Machine Learning |
| url | https://arxiv.org/abs/2311.03197 |