# Adaptive Safety with Control Barrier Functions

arXiv: https://arxiv.org/abs/1910.00555 · HTML: https://mlsanity.com/paper/1910.00555/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2019.

## Built on by (most cited first, 25 of 25)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [Safe Exploration in Model-based Reinforcement Learning using Control Barrier Functions](https://mlsanity.com/paper/2104.08171/) (2021)
- [Online Control Barrier Functions for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2303.04313/) (2023)
- [CBF-LLM: Safe Control for LLM Alignment](https://mlsanity.com/paper/2408.15625/) (2024)
- [Learning Control Barrier Functions and their application in Reinforcement Learning: A Survey](https://mlsanity.com/paper/2404.16879/) (2024)
- [Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions](https://mlsanity.com/paper/2207.14419/) (2022)
- [Implicit Safe Set Algorithm for Provably Safe Reinforcement Learning](https://mlsanity.com/paper/2405.02754/) (2024)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Robust Action Governor for Uncertain Piecewise Affine Systems with Non-convex Constraints and Safe Reinforcement Learning](https://mlsanity.com/paper/2207.08240/) (2022)
- [Safe Reinforcement Learning with Probabilistic Control Barrier Functions for Ramp Merging](https://mlsanity.com/paper/2212.00618/) (2022)
- [Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning](https://mlsanity.com/paper/2307.00828/) (2023)
- [Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models](https://mlsanity.com/paper/2402.18946/) (2024)
- [Enhanced Safety in Autonomous Driving: Integrating Latent State Diffusion Model for End-to-End Navigation](https://mlsanity.com/paper/2407.06317/) (2024)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)
- [Soft Actor-Critic-based Control Barrier Adaptation for Robust Autonomous Navigation in Unknown Environments](https://mlsanity.com/paper/2503.08479/) (2025)
- [Safe Uncertainty-Aware Learning of Robotic Suturing](https://mlsanity.com/paper/2505.16596/) (2025)
- [Safe Learning Reference Governor: Theory and Application to Fuel Truck Rollover Avoidance](https://mlsanity.com/paper/2101.09298/) (2021)
- [A stabilizing reinforcement learning approach for sampled systems with partially unknown models](https://mlsanity.com/paper/2208.14714/) (2022)
- [Adaptive MPC-based quadrupedal robot control under periodic disturbances](https://mlsanity.com/paper/2505.12361/) (2025)
- [Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures](https://mlsanity.com/paper/2505.19521/) (2025)
- [Control Barrier Function for Aligning Large Language Models](https://mlsanity.com/paper/2511.03121/) (2025)
- [Robust Taylor-Lagrange Control for Safety-Critical Systems](https://mlsanity.com/paper/2602.20076/) (2026)

## Abstract (arXiv)

Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunov-based methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the systems state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an adaptive cruise control (ACC) simulation.