Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161770276