# Control Barrier Functions: Theory and Applications

arXiv: https://arxiv.org/abs/1903.11199 · HTML: https://mlsanity.com/paper/1903.11199/

## Key facts

- Cited by 372 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2019.

## Built on by (most cited first, 30 of 372)

- [Safety Alignment Should Be Made More Than Just a Few Tokens Deep](https://mlsanity.com/paper/2406.05946/) (2024)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [ShieldAgent: Shielding Agents via Verifiable Safety Policy Reasoning](https://mlsanity.com/paper/2503.22738/) (2025)
- [Toward General-Purpose Robots via Foundation Models: A Survey and Meta-Analysis](https://mlsanity.com/paper/2312.08782/) (2023)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [PointWorld: Scaling 3D World Models for In-The-Wild Robotic Manipulation](https://mlsanity.com/paper/2601.03782/) (2026)
- [Safe Offline Reinforcement Learning with Feasibility-Guided Diffusion Model](https://mlsanity.com/paper/2401.10700/) (2024)
- [Safe Reinforcement Learning Using Robust Control Barrier Functions](https://mlsanity.com/paper/2110.05415/) (2021)
- [Reachability Constrained Reinforcement Learning](https://mlsanity.com/paper/2205.07536/) (2022)
- [safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Robotics](https://mlsanity.com/paper/2109.06325/) (2021)
- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [Learning Barrier Certificates: Towards Safe Reinforcement Learning with Zero Training-time Violations](https://mlsanity.com/paper/2108.01846/) (2021)
- [Iterative Reachability Estimation for Safe Reinforcement Learning](https://mlsanity.com/paper/2309.13528/) (2023)
- [Provably Safe Reinforcement Learning: Conceptual Analysis, Survey, and Benchmarking](https://mlsanity.com/paper/2205.06750/) (2022)
- [Empowering Autonomous Driving with Large Language Models: A Safety Perspective](https://mlsanity.com/paper/2312.00812/) (2023)
- [VLSA: Vision-Language-Action Models with Plug-and-Play Safety Constraint Layer](https://mlsanity.com/paper/2512.11891/) (2025)
- [Model-based Constrained Reinforcement Learning using Generalized Control Barrier Function](https://mlsanity.com/paper/2103.01556/) (2021)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Feasible Actor-Critic: Constrained Reinforcement Learning for Ensuring Statewise Safety](https://mlsanity.com/paper/2105.10682/) (2021)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [ISAACS: Iterative Soft Adversarial Actor-Critic for Safety](https://mlsanity.com/paper/2212.03228/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [A Survey on Physics Informed Reinforcement Learning: Review and Open Problems](https://mlsanity.com/paper/2309.01909/) (2023)
- [Safety Aware Task Planning via Large Language Models in Robotics](https://mlsanity.com/paper/2503.15707/) (2025)
- [Offline Goal-conditioned Reinforcement Learning with Quasimetric Representations](https://mlsanity.com/paper/2509.20478/) (2025)
- [Safe Occlusion-aware Autonomous Driving via Game-Theoretic Active Perception](https://mlsanity.com/paper/2105.08169/) (2021)
- [Learning Control Policies for Stochastic Systems with Reach-avoid Guarantees](https://mlsanity.com/paper/2210.05308/) (2022)
- [Safe Control with Neural Network Dynamic Models](https://mlsanity.com/paper/2110.01110/) (2021)

## Abstract (arXiv)

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.