Learning Diffeomorphic Lyapunov Functions from Data

Samuel Tesfazgi, Leonhard Sprandl, Sandra Hirche

Track: Extended abstract

Keywords: Diffeomorphism, Lyapunov function, Structure-preserving learning, Dynamical systems

TL;DR: A diffeomorphic learning framework is presented, where we learn structure-preserving transformations to augment simple, base functions with convenient geometric properties to obtain Lyapunov functions.

Abstract: 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.

Submission Number: 51