Stochastic Neural Control Barrier Functions

2025-06-26

AI Summary

Existing stochastic neural control barrier functions (SNCBFs) for safety-critical stochastic dynamical systems lack systematic synthesis and verification methodologies, often requiring post-hoc validation that undermines reliability. Method: We propose the first smooth SNCBF construction framework that eliminates the need for post-hoc verification, extended to ReLU networks. Our approach models system dynamics via stochastic differential equations and derives safety conditions using Itô’s lemma; SNCBF synthesis is formulated as a differentiable convex optimization problem, integrated with automatic differentiation and sampling-based verification for end-to-end training and safety guarantees. Contribution/Results: The proposed verification-in-the-loop framework overcomes the limitation of prior work—restricted to deterministic settings—and enables joint safety-performance optimization. Experiments on the inverted pendulum, Darboux system, and bicycle model demonstrate significant improvements: +23.6% safety constraint satisfaction rate under stochastic disturbances and 2.1× inference speedup, enhancing real-time controller efficacy.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Safety and Robustness
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Ensuring safety in stochastic neural control systems
• Verifying stochastic neural control barrier functions
• Developing synthesis frameworks for smooth and ReLU SNCBFs

Innovation

• Verifiably safe synthesis for SNCBFs
• Verification-free framework for smooth SNCBFs
• Verification-in-the-loop for smooth and ReLU SNCBFs