# Learning Feasibility Constraints for Control Barrier Functions

arXiv: https://arxiv.org/abs/2303.09403 · HTML: https://mlsanity.com/paper/2303.09403/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 10 Mar 2023.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach](https://mlsanity.com/paper/2003.04950/) (2020)
- [Control Barrier Functions for Systems with High Relative Degree](https://mlsanity.com/paper/1903.04706/) (2019)
- [Sufficient Conditions for Feasibility of Optimal Control Problems Using Control Barrier Functions](https://mlsanity.com/paper/2011.08248/) (2020)
- [Bridging the Gap between Optimal Trajectory Planning and Safety-Critical Control with Applications to Autonomous Vehicles](https://mlsanity.com/paper/2008.07632/) (2020)
- [Self-triggered Control for Safety Critical Systems using Control Barrier Functions](https://mlsanity.com/paper/1903.03692/) (2019)

## Built on by (most cited first, 2 of 2)

- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)

## Abstract (arXiv)

It has been shown that optimizing quadratic costs while stabilizing affine control systems to desired (sets of) states subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In this paper, we employ machine learning techniques to ensure the feasibility of these QPs, which is a challenging problem, especially for high relative degree constraints where High Order CBFs (HOCBFs) are required. To this end, we propose a sampling-based learning approach to learn a new feasibility constraint for CBFs; this constraint is then enforced by another HOCBF added to the QPs. The accuracy of the learned feasibility constraint is recursively improved by a recurrent training algorithm. We demonstrate the advantages of the proposed learning approach to constrained optimal control problems with specific focus on a robot control problem and on autonomous driving in an unknown environment.