Learning Diffeomorphic Lyapunov Functions from Data

The practical deployment of learning-based autonomous systems would greatly benefit from tools that flexibly obtain safety guarantees in the form of certificate functions from data. While the geometrical properties of such certificate functions are well understood, synthesizing them using machine learning techniques remains a challenge. To mitigate this issue, we propose a diffeomorphic function learning framework where prior structural knowledge regarding the desired output is encoded in a simple surrogate function, which is subsequently augmented through an expressive, topology-preserving state-space transformation. We demonstrate our approach by learning Lyapunov functions from real-world data and apply the method to different attractor systems.