Neural Control Barrier Functions from Physics Informed Neural Networks

2025-04-15

AI Summary

Manually designing Control Barrier Functions (CBFs) for high-dimensional autonomous systems is challenging, and conventional CBFs lack flexibility in defining safety regions. Method: This paper proposes a physics-informed neural network (PINN) framework guided by the Zubov partial differential equation (PDE) to automatically synthesize provably safe neural CBFs. The Zubov equation is enforced as a hard constraint during training, and a reciprocal CBF parameterization—replacing the standard zeroing form—is adopted to enhance expressivity and scalability to high dimensions. Crucially, the method supports user-defined, arbitrarily shaped safety sets without requiring explicit PDE solving. Results: Evaluated on inverted pendulum stabilization, autonomous vehicle obstacle avoidance, and complex UAV navigation, the approach delivers rigorous safety guarantees, significantly improving CBF synthesis efficiency and cross-task generalizability.

Technology Category

• Natural Language Processing: Safety and Robustness
• Computer Vision: Low Level & Physics-based Vision
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

As autonomous systems become increasingly prevalent in daily life, ensuring their safety is paramount. Control Barrier Functions (CBFs) have emerged as an effective tool for guaranteeing safety; however, manually designing them for specific applications remains a significant challenge. With the advent of deep learning techniques, recent research has explored synthesizing CBFs using neural networks-commonly referred to as neural CBFs. This paper introduces a novel class of neural CBFs that leverages a physics-inspired neural network framework by incorporating Zubov's Partial Differential Equation (PDE) within the context of safety. This approach provides a scalable methodology for synthesizing neural CBFs applicable to high-dimensional systems. Furthermore, by utilizing reciprocal CBFs instead of zeroing CBFs, the proposed framework allows for the specification of flexible, user-defined safe regions. To validate the effectiveness of the approach, we present case studies on three different systems: an inverted pendulum, autonomous ground navigation, and aerial navigation in obstacle-laden environments.

Problem

• Automating safety design for autonomous systems using neural networks
• Scaling neural Control Barrier Functions for high-dimensional systems
• Enabling flexible safe region specification via reciprocal CBFs

Innovation

• Physics-inspired neural network framework
• Zubov's PDE for safety synthesis
• Reciprocal CBFs for flexible safe regions