Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions
For control engineers and researchers, this method provides a way to certify stability regions from limited data, though it is incremental over existing Lyapunov-based approaches.
The paper presents a data-driven method to approximate regions of attraction for unknown nonlinear systems using linear programming to select piecewise affine Lyapunov functions, achieving certified regions from sparse data.
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 \ac{PWA} 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.