Stability-Certified Learning of Control Systems with Quadratic Nonlinearities
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909125256937472 |
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| author | Duff, Igor Pontes Goyal, Pawan Benner, Peter |
| author_facet | Duff, Igor Pontes Goyal, Pawan Benner, Peter |
| contents | This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability is a fundamental attribute of dynamical systems, yet it is not always assured in models derived through inference. Our main objective is to develop a method that facilitates the inference of quadratic control dynamical systems with inherent stability guarantees. To this aim, we investigate the stability characteristics of control systems with energy-preserving nonlinearities, thereby identifying conditions under which such systems are bounded-input bounded-state stable. These insights are subsequently applied to the learning process, yielding inferred models that are inherently stable by design. The efficacy of our proposed framework is demonstrated through a couple of numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability-Certified Learning of Control Systems with Quadratic Nonlinearities Duff, Igor Pontes Goyal, Pawan Benner, Peter Machine Learning Dynamical Systems Optimization and Control This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability is a fundamental attribute of dynamical systems, yet it is not always assured in models derived through inference. Our main objective is to develop a method that facilitates the inference of quadratic control dynamical systems with inherent stability guarantees. To this aim, we investigate the stability characteristics of control systems with energy-preserving nonlinearities, thereby identifying conditions under which such systems are bounded-input bounded-state stable. These insights are subsequently applied to the learning process, yielding inferred models that are inherently stable by design. The efficacy of our proposed framework is demonstrated through a couple of numerical examples. |
| title | Stability-Certified Learning of Control Systems with Quadratic Nonlinearities |
| topic | Machine Learning Dynamical Systems Optimization and Control |
| url | https://arxiv.org/abs/2403.00646 |