Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914583081385984 |
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| author | Khattabi, Oumayma Tacchi-Bénard, Matteo Gulan, Martin Olaru, Sorin |
| author_facet | Khattabi, Oumayma Tacchi-Bénard, Matteo Gulan, Martin Olaru, Sorin |
| contents | This paper presents a method to approximate regions of attraction of unknown nonlinear dynamical systems from data. Assuming point-wise evaluations of the vector field and known Lipschitz bounds, a polyhedral uncertainty set of admissible dynamics is constructed. This uncertainty description enables the synthesis of a continuous piece-wise affine Lyapunov candidate via a linear program, enforcing a robust decrease condition for all admissible vector fields. The approach allows certification of a region of attraction consistent with the available data. Numerical examples illustrate the effectiveness of the proposed method in extracting certified regions of attraction from sparse data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19961 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions Khattabi, Oumayma Tacchi-Bénard, Matteo Gulan, Martin Olaru, Sorin Optimization and Control Systems and Control This paper presents a method to approximate regions of attraction of unknown nonlinear dynamical systems from data. Assuming point-wise evaluations of the vector field and known Lipschitz bounds, a polyhedral uncertainty set of admissible dynamics is constructed. This uncertainty description enables the synthesis of a continuous piece-wise affine Lyapunov candidate via a linear program, enforcing a robust decrease condition for all admissible vector fields. The approach allows certification of a region of attraction consistent with the available data. Numerical examples illustrate the effectiveness of the proposed method in extracting certified regions of attraction from sparse data. |
| title | Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2605.19961 |