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arXiv · 2605.19961

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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Oumayma Khattabi, Matteo Tacchi-Bénard, Martin Gulan, Sorin Olaru. 2026-05-19. Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions. https://arxiv.org/abs/2605.19961

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