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PreprintCC BY 4.0arXiv

Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions

  • Oumayma Khattabi
  • Matteo Tacchi-Bénard
  • Martin Gulan
  • Sorin Olaru
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{khattabi2026datadriven,
  title = {{Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions}},
  author = {Oumayma Khattabi and Matteo Tacchi-Bénard and Martin Gulan and Sorin Olaru},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.19961},
  eprint = {2605.19961},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.19961},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions
AU  - Oumayma Khattabi
AU  - Matteo Tacchi-Bénard
AU  - Martin Gulan
AU  - Sorin Olaru
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2605.19961
UR  - https://arxiv.org/abs/2605.19961
AB  - 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.
ER  -