Data-Driven Learning of Safety-Critical Control with Stochastic Control Barrier Functions

TL;DR

This paper introduces a data-driven framework for safety-critical control of stochastic systems with unknown noise components, using supervised learning to approximate stochastic dynamics and ensure safety guarantees.

Contribution

It proposes the DDSCBF method that learns unknown stochastic dynamics and maintains safety guarantees without prior knowledge of the stochastic component.

Findings

The DDSCBF scheme can approximate the Itô derivative of the stochastic control barrier function.

Safety guarantees are maintained using DDSCBF even with unknown stochastic dynamics.

Validation on two nonlinear stochastic systems confirms the effectiveness of the approach.

Abstract

Control barrier functions are widely used to synthesize safety-critical controls. The existence of Gaussian-type noise may lead to unsafe actions and result in severe consequences. While studies are widely done in safety-critical control for stochastic systems, in many real-world applications, we do not have the knowledge of the stochastic component of the dynamics. In this paper, we study safety-critical control of stochastic systems with an unknown diffusion part and propose a data-driven method to handle these scenarios. More specifically, we propose a data-driven stochastic control barrier function (DDSCBF) framework and use supervised learning to learn the unknown stochastic dynamics via the DDSCBF scheme. Under some reasonable assumptions, we provide guarantees that the DDSCBF scheme can approximate the It\^{o} derivative of the stochastic control barrier function (SCBF) under partially unknown dynamics using the universal approximation theorem. We also show that we can achieve the same safety guarantee using the DDSCBF scheme as with SCBF in previous work without requiring the knowledge of stochastic dynamics. We use two non-linear stochastic systems to validate our theory in simulations.