Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation

TL;DR

This paper introduces a symbolic verification framework for neural control barrier functions using derivative bounds propagation, improving efficiency and accuracy in safety verification for robot systems.

Contribution

It presents a novel symbolic verification method for ReLU-based neural CBFs that combines derivative bounds with system dynamics, outperforming existing interval arithmetic methods.

Findings

Outperforms interval arithmetic baselines in verified rate

Reduces verification time significantly

Effective across various robot dynamics

Abstract

Control barrier functions (CBFs) are important in safety-critical systems and robot control applications. Neural networks have been used to parameterize and synthesize CBFs with bounded control input for complex systems. However, it is still challenging to verify pre-trained neural networks CBFs (neural CBFs) in an efficient symbolic manner. To this end, we propose a new efficient verification framework for ReLU-based neural CBFs through symbolic derivative bound propagation by combining the linearly bounded nonlinear dynamic system and the gradient bounds of neural CBFs. Specifically, with Heaviside step function form for derivatives of activation functions, we show that the symbolic bounds can be propagated through the inner product of neural CBF Jacobian and nonlinear system dynamics. Through extensive experiments on different robot dynamics, our results outperform the interval arithmetic based baselines in verified rate and verification time along the CBF boundary, validating the effectiveness and efficiency of the proposed method with different model complexity. The code can be found at https://github.com/intelligent-control-lab/ verify-neural-CBF.