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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2605.18292 |
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| _version_ | 1866909054170824704 |
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| author | Frank, Daniel Shakib, Fahim Staab, Steffen |
| author_facet | Frank, Daniel Shakib, Fahim Staab, Steffen |
| contents | This paper presents a method that learns a regionally stable recurrent neural network model from a set of input-output data generated by an unknown dynamical system. Relying on generalized sector conditions on the deadzone activation function, we first derive sufficient conditions that guarantee forward invariance on a compact set of the state space for any inputs from a given set. Such regional properties lead to less conservative conditions compared to variants that offer a global form of stability, and are in line with the system data that is only observed regionally. Our learning method derives conditions for regional stability using a barrier function approach, leading to models equipped with a certificate of regional stability in a subset of the state space and for a given input set. We illustrate our theoretical result with a numerical example and compare it to methods that impose a global form of stability, which fail to identify the system, and with a method that imposes no stability constraints at all, which does not guarantee a stable behavior within any state or input set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18292 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning the dynamics of nonlinear systems with regional stability guarantees through linear matrix inequality constraints Frank, Daniel Shakib, Fahim Staab, Steffen Systems and Control This paper presents a method that learns a regionally stable recurrent neural network model from a set of input-output data generated by an unknown dynamical system. Relying on generalized sector conditions on the deadzone activation function, we first derive sufficient conditions that guarantee forward invariance on a compact set of the state space for any inputs from a given set. Such regional properties lead to less conservative conditions compared to variants that offer a global form of stability, and are in line with the system data that is only observed regionally. Our learning method derives conditions for regional stability using a barrier function approach, leading to models equipped with a certificate of regional stability in a subset of the state space and for a given input set. We illustrate our theoretical result with a numerical example and compare it to methods that impose a global form of stability, which fail to identify the system, and with a method that imposes no stability constraints at all, which does not guarantee a stable behavior within any state or input set. |
| title | Learning the dynamics of nonlinear systems with regional stability guarantees through linear matrix inequality constraints |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.18292 |