Learning Stability Certificates from Data

TL;DR

This paper introduces algorithms to learn stability certificates directly from trajectory data, enabling stability verification for complex systems without requiring explicit models, and provides theoretical guarantees for their generalization.

Contribution

It develops data-driven methods for learning stability certificates from trajectories, with bounds on generalization error and applications to control tasks.

Findings

Certificates can be learned efficiently for complex dynamics.

Learned certificates provide stability guarantees.

Applications include adaptive control.

Abstract

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property. However, algorithms for synthesizing certificate functions typically require a closed-form analytical expression of the underlying dynamics, which rules out their use on many modern robotic platforms. To circumvent this issue, we develop algorithms for learning certificate functions only from trajectory data. We establish bounds on the generalization error - the probability that a certificate will not certify a new, unseen trajectory - when learning from trajectories, and we convert such generalization error bounds into global stability guarantees. We demonstrate empirically that certificates for complex dynamics can be efficiently learned, and that the learned certificates can be used for downstream tasks such as adaptive control.