Robustly Learning Regions of Attraction from Fixed Data

TL;DR

This paper introduces a data-driven method to learn regions of attraction for control systems without requiring explicit models, using a Lyapunov function learned from fixed data, enhancing robustness and computational efficiency.

Contribution

It proposes a novel Lyapunov analysis framework that learns a piece-wise affine Lyapunov function from fixed data, without model reliance, and extends classical stability criteria for iterative region of attraction estimation.

Findings

Learnt Lyapunov function is robust to dynamics consistent with data.

Region of attraction can be iteratively expanded using the proposed method.

The approach relies on second order cone programming for computation.

Abstract

While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity simulator representing the system at hand. In this work, a new data-driven Lyapunov analysis framework is proposed. Without using the model or its simulator, the proposed approach can learn a piece-wise affine Lyapunov function with a finite and fixed off-line dataset. The learnt Lyapunov function is robust to any dynamics that are consistent with the off-line dataset, and its computation is based on second order cone programming. Along with the development of the proposed scheme, a slight generalization of classical Lyapunov stability criteria is derived, enabling an iterative inference algorithm to augment the region of attraction.