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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.03493 |
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| _version_ | 1866918011398520832 |
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| author | Khattabi, Oumayma Tacchi-Bénard, Matteo Olaru, Sorin |
| author_facet | Khattabi, Oumayma Tacchi-Bénard, Matteo Olaru, Sorin |
| contents | The paper is dedicated to data-driven analysis of dynamical systems. It deals with certifying the basin of attraction of a stable equilibrium for an unknown dynamical system. It is supposed that point-wise evaluation of the right-hand side of the ordinary differential equation governing the system is available for a set of points in the state space. Technically, a Piecewise Affine Lyapunov function will be constructed iteratively using an optimisation-based technique for the effective validation of the certificates. As a main contribution, whenever those certificates are violated locally, a refinement of the domain and the associated tessellation is produced, thus leading to an improvement in the description of the domain of attraction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequentially learning regions of attraction from data Khattabi, Oumayma Tacchi-Bénard, Matteo Olaru, Sorin Systems and Control The paper is dedicated to data-driven analysis of dynamical systems. It deals with certifying the basin of attraction of a stable equilibrium for an unknown dynamical system. It is supposed that point-wise evaluation of the right-hand side of the ordinary differential equation governing the system is available for a set of points in the state space. Technically, a Piecewise Affine Lyapunov function will be constructed iteratively using an optimisation-based technique for the effective validation of the certificates. As a main contribution, whenever those certificates are violated locally, a refinement of the domain and the associated tessellation is produced, thus leading to an improvement in the description of the domain of attraction. |
| title | Sequentially learning regions of attraction from data |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2505.03493 |