# Learning for Safety-Critical Control with Control Barrier Functions

arXiv: https://arxiv.org/abs/1912.10099 · HTML: https://mlsanity.com/paper/1912.10099/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2019.

## Built on by (most cited first, 30 of 69)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environments](https://mlsanity.com/paper/2209.15090/) (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)
- [Provably Safe Reinforcement Learning: Conceptual Analysis, Survey, and Benchmarking](https://mlsanity.com/paper/2205.06750/) (2022)
- [Safe Driving via Expert Guided Policy Optimization](https://mlsanity.com/paper/2110.06831/) (2021)
- [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)
- [Distributional Depth-Based Estimation of Object Articulation Models](https://mlsanity.com/paper/2108.05875/) (2021)
- [Safe Reinforcement Learning of Dynamic High-Dimensional Robotic Tasks: Navigation, Manipulation, Interaction](https://mlsanity.com/paper/2209.13308/) (2022)
- [Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions](https://mlsanity.com/paper/2301.01526/) (2023)
- [Safe Exploration by Solving Early Terminated MDP](https://mlsanity.com/paper/2107.04200/) (2021)
- [Safe Reinforcement Learning on the Constraint Manifold: Theory and Applications](https://mlsanity.com/paper/2404.09080/) (2024)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise](https://mlsanity.com/paper/2110.12662/) (2021)
- [Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control](https://mlsanity.com/paper/2109.08947/) (2021)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanes](https://mlsanity.com/paper/2402.05279/) (2024)
- [Safe Exploration in Model-based Reinforcement Learning using Control Barrier Functions](https://mlsanity.com/paper/2104.08171/) (2021)
- [Model-based Dynamic Shielding for Safe and Efficient Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2304.06281/) (2023)
- [Youla-REN: Learning Nonlinear Feedback Policies with Robust Stability Guarantees](https://mlsanity.com/paper/2112.01253/) (2021)
- [Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Driving](https://mlsanity.com/paper/2203.02401/) (2022)
- [End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functions](https://mlsanity.com/paper/2212.11365/) (2022)
- [Constrained Diffusers for Safe Planning and Control](https://mlsanity.com/paper/2506.12544/) (2025)
- [Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments](https://mlsanity.com/paper/2201.01347/) (2022)
- [Sequential Neural Barriers for Scalable Dynamic Obstacle Avoidance](https://mlsanity.com/paper/2307.03015/) (2023)
- [Maximum diffusion reinforcement learning](https://mlsanity.com/paper/2309.15293/) (2023)
- [Multi-Agent Reinforcement Learning Guided by Signal Temporal Logic Specifications](https://mlsanity.com/paper/2306.06808/) (2023)
- [A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stability](https://mlsanity.com/paper/2110.00693/) (2021)
- [Safe Reinforcement Learning via Confidence-Based Filters](https://mlsanity.com/paper/2207.01337/) (2022)

## Abstract (arXiv)

Modern nonlinear control theory seeks to endow systems with properties of stability and safety, and have been deployed successfully in multiple domains. Despite this success, model uncertainty remains a significant challenge in synthesizing safe controllers, leading to degradation in the properties provided by the controllers. This paper develops a machine learning framework utilizing Control Barrier Functions (CBFs) to reduce model uncertainty as it impact the safe behavior of a system. This approach iteratively collects data and updates a controller, ultimately achieving safe behavior. We validate this method in simulation and experimentally on a Segway platform.