Stochastic Neural Control Barrier Functions

TL;DR

This paper introduces methods for the safe synthesis and verification of stochastic neural control barrier functions, extending safety guarantees to stochastic systems using neural network representations.

Contribution

It presents a verification-free synthesis framework for smooth SNCBFs and a verification-in-the-loop approach for ReLU SNCBFs, addressing a gap in stochastic safety verification.

Findings

Validated frameworks on inverted pendulum, Darboux, and unicycle models.

Extended neural CBFs to stochastic systems with safety guarantees.

Demonstrated effectiveness of the proposed methods in multiple control scenarios.

Abstract

Control Barrier Functions (CBFs) are utilized to ensure the safety of control systems. CBFs act as safety filters in order to provide safety guarantees without compromising system performance. These safety guarantees rely on the construction of valid CBFs. Due to their complexity, CBFs can be represented by neural networks, known as neural CBFs (NCBFs). Existing works on the verification of the NCBF focus on the synthesis and verification of NCBFs in deterministic settings, leaving the stochastic NCBFs (SNCBFs) less studied. In this work, we propose a verifiably safe synthesis for SNCBFs. We consider the cases of smooth SNCBFs with twice-differentiable activation functions and SNCBFs that utilize the Rectified Linear Unit or ReLU activation function. We propose a verification-free synthesis framework for smooth SNCBFs and a verification-in-the-loop synthesis framework for both smooth and ReLU SNCBFs. and we validate our frameworks in three cases, namely, the inverted pendulum, Darboux, and the unicycle model.