Scalable Verification of Neural Control Barrier Functions Using Linear Bound Propagation

arXiv cs.RO / 4/15/2026

💬 OpinionIdeas & Deep AnalysisModels & Research

共有:

Key Points

The paper addresses a key bottleneck in safety certification of neural-network-based control barrier functions (CBFs): efficiently verifying that a trained neural network satisfies the required CBF conditions.
It proposes a scalable verification framework built on linear bound propagation (LBP), extended to bound network gradients and combined with McCormick relaxation to form linear upper and lower bounds on CBF conditions.
The method is designed to work for arbitrary control-affine dynamical systems and supports a wide range of nonlinear activation functions.
To improve tightness, the authors introduce a parallelizable adaptive refinement strategy that reduces conservatism by refining the regions used for bound computation.
Numerical experiments suggest the approach can verify substantially larger neural networks than existing CBF verification methods.

Abstract

Control barrier functions (CBFs) are a popular tool for safety certification of nonlinear dynamical control systems. Recently, CBFs represented as neural networks have shown great promise due to their expressiveness and applicability to a broad class of dynamics and safety constraints. However, verifying that a trained neural network is indeed a valid CBF is a computational bottleneck that limits the size of the networks that can be used. To overcome this limitation, we present a novel framework for verifying neural CBFs based on piecewise linear upper and lower bounds on the conditions required for a neural network to be a CBF. Our approach is rooted in linear bound propagation (LBP) for neural networks, which we extend to compute bounds on the gradients of the network. Combined with McCormick relaxation, we derive linear upper and lower bounds on the CBF conditions, thereby eliminating the need for computationally expensive verification procedures. Our approach applies to arbitrary control-affine systems and a broad range of nonlinear activation functions. To reduce conservatism, we develop a parallelizable refinement strategy that adaptively refines the regions over which these bounds are computed. Our approach scales to larger neural networks than state-of-the-art verification procedures for CBFs, as demonstrated by our numerical experiments.