# Safety-Critical Control using Optimal-decay Control Barrier Function with Guaranteed Point-wise Feasibility

arXiv: https://arxiv.org/abs/2103.12375 · HTML: https://mlsanity.com/paper/2103.12375/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2021.

## Built on by (most cited first, 7 of 7)

- [Safe Reinforcement Learning Using Robust Control Barrier Functions](https://mlsanity.com/paper/2110.05415/) (2021)
- [ISAACS: Iterative Soft Adversarial Actor-Critic for Safety](https://mlsanity.com/paper/2212.03228/) (2022)
- [Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments](https://mlsanity.com/paper/2201.01347/) (2022)
- [Differentiable Safe Controller Design through Control Barrier Functions](https://mlsanity.com/paper/2209.10034/) (2022)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [Learning Adaptive Safety for Multi-Agent Systems](https://mlsanity.com/paper/2309.10657/) (2023)
- [Safe model-based Reinforcement Learning via Model Predictive Control and Control Barrier Functions](https://mlsanity.com/paper/2512.04856/) (2025)

## Abstract (arXiv)

Safety is one of the fundamental problems in robotics. Recently, a quadratic program-based control barrier function (CBF) method has emerged as a way to enforce safety-critical constraints. Together with control Lyapunov function (CLF), it forms a safety-critical control strategy, named CLF-CBF-QP, which can mediate between achieving the control objective and ensuring safety, while being executable in real-time. However, once additional constraints such as input constraints are introduced, the CLF-CBF-QP may encounter infeasibility. In order to address the challenge that arises due to the infeasibility, we propose an optimal-decay form for safety-critical control wherein the decay rate of the CBF is optimized point-wise in time so as to guarantee point-wise feasibility when the state lies inside the safe set. The proposed control design is numerically validated using an adaptive cruise control example.