# Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach

arXiv: https://arxiv.org/abs/2003.04950 · HTML: https://mlsanity.com/paper/2003.04950/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2020.

## Built on by (most cited first, 30 of 35)

- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [VLSA: Vision-Language-Action Models with Plug-and-Play Safety Constraint Layer](https://mlsanity.com/paper/2512.11891/) (2025)
- [Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learning](https://mlsanity.com/paper/2111.07695/) (2021)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution States](https://mlsanity.com/paper/2301.12012/) (2023)
- [Learning Robust Hybrid Control Barrier Functions for Uncertain Systems](https://mlsanity.com/paper/2101.06492/) (2021)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions](https://mlsanity.com/paper/2509.24243/) (2025)
- [Sequential Neural Barriers for Scalable Dynamic Obstacle Avoidance](https://mlsanity.com/paper/2307.03015/) (2023)
- [How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraints](https://mlsanity.com/paper/2511.18606/) (2025)
- [Learning Control Barrier Functions and their application in Reinforcement Learning: A Survey](https://mlsanity.com/paper/2404.16879/) (2024)
- [Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Control](https://mlsanity.com/paper/2502.03640/) (2025)
- [Reactive and Safe Road User Simulations using Neural Barrier Certificates](https://mlsanity.com/paper/2109.06689/) (2021)
- [Provably Correct Training of Neural Network Controllers Using Reachability Analysis](https://mlsanity.com/paper/2102.10806/) (2021)
- [Safe Reach Set Computation via Neural Barrier Certificates](https://mlsanity.com/paper/2404.18813/) (2024)
- [Model Free Barrier Functions via Implicit Evading Maneuvers](https://mlsanity.com/paper/2107.12871/) (2021)
- [Safe Inverse Reinforcement Learning via Control Barrier Function](https://mlsanity.com/paper/2212.02753/) (2022)
- [ConBaT: Control Barrier Transformer for Safe Policy Learning](https://mlsanity.com/paper/2303.04212/) (2023)
- [Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments](https://mlsanity.com/paper/2410.20267/) (2024)
- [Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions](https://mlsanity.com/paper/2505.11755/) (2025)
- [Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safety](https://mlsanity.com/paper/2203.15474/) (2022)
- [Learning Feasibility Constraints for Control Barrier Functions](https://mlsanity.com/paper/2303.09403/) (2023)
- [ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks](https://mlsanity.com/paper/2509.16614/) (2025)
- [Safety-Critical Learning of Robot Control with Temporal Logic Specifications](https://mlsanity.com/paper/2109.02791/) (2021)
- [EnergyShield: Provably-Safe Offloading of Neural Network Controllers for Energy Efficiency](https://mlsanity.com/paper/2302.06572/) (2023)
- [Online Efficient Safety-Critical Control for Mobile Robots in Unknown Dynamic Multi-Obstacle Environments](https://mlsanity.com/paper/2402.16449/) (2024)
- [ABNet: Attention BarrierNet for Safe and Scalable Robot Learning](https://mlsanity.com/paper/2406.13025/) (2024)
- [Accelerated Learning with Linear Temporal Logic using Differentiable Simulation](https://mlsanity.com/paper/2506.01167/) (2025)
- [Geometry of Radial Basis Neural Networks for Safety Biased Approximation of Unsafe Regions](https://mlsanity.com/paper/2210.05596/) (2022)
- [Assurance for Deployed Continual Learning Systems](https://mlsanity.com/paper/2311.10787/) (2023)

## Abstract (arXiv)

Control barrier functions are mathematical constructs used to guarantee safety for robotic systems. When integrated as constraints in a quadratic programming optimization problem, instantaneous control synthesis with real-time performance demands can be achieved for robotics applications. Prevailing use has assumed full knowledge of the safety barrier functions, however there are cases where the safe regions must be estimated online from sensor measurements. In these cases, the corresponding barrier function must be synthesized online. This paper describes a learning framework for estimating control barrier functions from sensor data. Doing so affords system operation in unknown state space regions without compromising safety. Here, a support vector machine classifier provides the barrier function specification as determined by sets of safe and unsafe states obtained from sensor measurements. Theoretical safety guarantees are provided. Experimental ROS-based simulation results for an omnidirectional robot equipped with LiDAR demonstrate safe operation.