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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.28502 |
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| _version_ | 1866910087340097536 |
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| author | Bierwart, François-Grégoire Mauroy, Alexandre |
| author_facet | Bierwart, François-Grégoire Mauroy, Alexandre |
| contents | In this paper, we develop a comprehensive framework to estimate regions of attraction of equilibria for dynamics associated with general vector fields. This framework combines Koopman operator-based methods with rigorous validation techniques. A candidate Lyapunov function is constructed with approximated Koopman eigenfunctions and further validated through polynomial approximation, either with SOS-based techniques or with a worst-case approach using an adaptive grid. The framework is general, not only since it is adapted to non-polynomial vector fields, but also since the Koopman operator can be approximated with general bases yielding non-polynomial Lyapunov functions. The performance of the method is illustrated with several numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28502 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A numerical Koopman-based framework to estimate regions of attraction for general vector fields Bierwart, François-Grégoire Mauroy, Alexandre Dynamical Systems In this paper, we develop a comprehensive framework to estimate regions of attraction of equilibria for dynamics associated with general vector fields. This framework combines Koopman operator-based methods with rigorous validation techniques. A candidate Lyapunov function is constructed with approximated Koopman eigenfunctions and further validated through polynomial approximation, either with SOS-based techniques or with a worst-case approach using an adaptive grid. The framework is general, not only since it is adapted to non-polynomial vector fields, but also since the Koopman operator can be approximated with general bases yielding non-polynomial Lyapunov functions. The performance of the method is illustrated with several numerical examples. |
| title | A numerical Koopman-based framework to estimate regions of attraction for general vector fields |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2603.28502 |