arXiv subjects

Oumayma Khattabi

Publications and source records attributed to Oumayma Khattabi.

3 recordsLinked to original sources

arXiv2026

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

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.

math.OC↗

arXiv2025

Convex computation of regions of attraction from data using Sums-of-Squares programming

This paper focuses on the analysis of the Region of Attraction (RoA) for unknown autonomous dynamical systems. A data-driven approach based on the moment-Sum-of-Squares (SoS) hierarchy is proposed, enabling novel RoA outer approximations despite the reduced information on the dynamics. The main contribution consists of bypassing the system model and, hence, the recurring constraint on its polynomial structure. Numerical experiments showcase the influence of data on learned approximating sets, highlighting the potential of this method.

eess.SY↗

arXiv2025

Sequentially learning regions of attraction from data

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.

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