# Learning Hybrid Control Barrier Functions from Data

arXiv: https://arxiv.org/abs/2011.04112 · HTML: https://mlsanity.com/paper/2011.04112/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2020.

## Built on by (most cited first, 24 of 24)

- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environments](https://mlsanity.com/paper/2209.15090/) (2022)
- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Steering Dialogue Dynamics for Robustness against Multi-turn Jailbreaking Attacks](https://mlsanity.com/paper/2503.00187/) (2025)
- [Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imagination](https://mlsanity.com/paper/2405.00846/) (2024)
- [Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approach](https://mlsanity.com/paper/2302.00171/) (2023)
- [Learning Robust Hybrid Control Barrier Functions for Uncertain Systems](https://mlsanity.com/paper/2101.06492/) (2021)
- [Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation](https://mlsanity.com/paper/2410.16281/) (2024)
- [Joint Differentiable Optimization and Verification for Certified Reinforcement Learning](https://mlsanity.com/paper/2201.12243/) (2022)
- [Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings](https://mlsanity.com/paper/2403.10497/) (2024)
- [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)
- [Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees](https://mlsanity.com/paper/2403.07308/) (2024)
- [Learning Globally Smooth Functions on Manifolds](https://mlsanity.com/paper/2210.00301/) (2022)
- [LMI-Net: Linear Matrix Inequality--Constrained Neural Networks via Differentiable Projection Layers](https://mlsanity.com/paper/2604.05374/) (2026)
- [Safe Inverse Reinforcement Learning via Control Barrier Function](https://mlsanity.com/paper/2212.02753/) (2022)
- [Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics](https://mlsanity.com/paper/2212.00679/) (2022)
- [Safe PDE Boundary Control with Neural Operators](https://mlsanity.com/paper/2411.15643/) (2024)
- [Failing with Grace: Learning Neural Network Controllers that are Boundedly Unsafe](https://mlsanity.com/paper/2106.11881/) (2021)
- [Fault Tolerant Neural Control Barrier Functions for Robotic Systems under Sensor Faults and Attacks](https://mlsanity.com/paper/2402.18677/) (2024)
- [Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem](https://mlsanity.com/paper/2411.15972/) (2024)
- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)
- [Safe Probabilistic Planning for Human-Robot Interaction using Conformal Risk Control](https://mlsanity.com/paper/2603.10392/) (2026)

## Abstract (arXiv)

Motivated by the lack of systematic tools to obtain safe control laws for hybrid systems, we propose an optimization-based framework for learning certifiably safe control laws from data. In particular, we assume a setting in which the system dynamics are known and in which data exhibiting safe system behavior is available. We propose hybrid control barrier functions for hybrid systems as a means to synthesize safe control inputs. Based on this notion, we present an optimization-based framework to learn such hybrid control barrier functions from data. Importantly, we identify sufficient conditions on the data such that feasibility of the optimization problem ensures correctness of the learned hybrid control barrier functions, and hence the safety of the system. We illustrate our findings in two simulations studies, including a compass gait walker.