Scalable synthesis of safety certificates from data with application to learning-based control

TL;DR

This paper presents scalable methods for synthesizing safety certificates in learning-based control systems using convex optimization and Gaussian processes, enabling safer and more efficient control of complex systems.

Contribution

It introduces two novel scalable techniques for safety set synthesis: one using approximate linear models and Lipschitz continuity, and another incorporating Gaussian process priors to reduce conservatism.

Findings

Methods improve scalability for safety certification

Gaussian process approach reduces conservatism in safe sets

Numerical examples demonstrate effectiveness in vehicle control

Abstract

The control of complex systems faces a trade-off between high performance and safety guarantees, which in particular restricts the application of learning-based methods to safety-critical systems. A recently proposed framework to address this issue is the use of a safety controller, which guarantees to keep the system within a safe region of the state space. This paper introduces efficient techniques for the synthesis of a safe set and control law, which offer improved scalability properties by relying on approximations based on convex optimization problems. The first proposed method requires only an approximate linear system model and Lipschitz continuity of the unknown nonlinear dynamics. The second method extends the results by showing how a Gaussian process prior on the unknown system dynamics can be used in order to reduce conservatism of the resulting safe set. We demonstrate the results with numerical examples, including an autonomous convoy of vehicles.