# Refining Control Barrier Functions through Hamilton-Jacobi Reachability

arXiv: https://arxiv.org/abs/2204.12507 · HTML: https://mlsanity.com/paper/2204.12507/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2022.

## Built on by (most cited first, 15 of 15)

- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraints](https://mlsanity.com/paper/2511.18606/) (2025)
- [Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networks](https://mlsanity.com/paper/2506.15693/) (2025)
- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safety](https://mlsanity.com/paper/2407.00616/) (2024)
- [Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions](https://mlsanity.com/paper/2505.11755/) (2025)
- [Off Policy Lyapunov Stability in Reinforcement Learning](https://mlsanity.com/paper/2509.09863/) (2025)
- [ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks](https://mlsanity.com/paper/2509.16614/) (2025)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)
- [Pre-Trained Vision Models as Perception Backbones for Safety Filters in Autonomous Driving](https://mlsanity.com/paper/2410.22585/) (2024)
- [Learning Neural Control Barrier Functions from Expert Demonstrations using Inverse Constraint Learning](https://mlsanity.com/paper/2510.21560/) (2025)
- [DualShield: Safe Model Predictive Diffusion via Reachability Analysis for Interactive Autonomous Driving](https://mlsanity.com/paper/2601.15729/) (2026)
- [Provably Safe, Yet Scalable Reinforcement Learning](https://mlsanity.com/paper/2606.14536/) (2026)
- [Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllers](https://mlsanity.com/paper/2504.08249/) (2025)
- [LEAP-CBF: A Safety Filter for Uncertain Systems with Least-Effort Adversarial Potentials](https://mlsanity.com/paper/2609.28364/) (2026)

## Abstract (arXiv)

Safety filters based on Control Barrier Functions (CBFs) have emerged as a practical tool for the safety-critical control of autonomous systems. These approaches encode safety through a value function and enforce safety by imposing a constraint on the time derivative of this value function. However, synthesizing a valid CBF that is not overly conservative in the presence of input constraints is a notorious challenge. In this work, we propose refining a candidate CBF using formal verification methods to obtain a valid CBF. In particular, we update an expert-synthesized or backup CBF using dynamic programming (DP) based reachability analysis. Our framework, refineCBF, guarantees that with every DP iteration the obtained CBF is provably at least as safe as the prior iteration and converges to a valid CBF. Therefore, refineCBF can be used in-the-loop for robotic systems. We demonstrate the practicality of our method to enhance safety and/or reduce conservativeness on a range of nonlinear control-affine systems using various CBF synthesis techniques in simulation.