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

TL;DR

This paper introduces a data-driven LP-based method to approximate regions of attraction for unknown nonlinear systems using PWA Lyapunov functions and sparse data.

Contribution

It proposes a novel LP-based approach to synthesize Lyapunov functions from data, enabling certified region of attraction estimation.

Findings

Effective extraction of certified regions of attraction from sparse data.

Robust Lyapunov functions synthesized via linear programming.

Numerical examples demonstrate practical applicability.

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.