# Compatibility checking of multiple control barrier functions for input constrained systems

arXiv: https://arxiv.org/abs/2209.02284 · HTML: https://mlsanity.com/paper/2209.02284/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2022.

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

- [Learning Adaptive Safety for Multi-Agent Systems](https://mlsanity.com/paper/2309.10657/) (2023)
- [Sample Efficient Certification of Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2509.03899/) (2025)

## Abstract (arXiv)

State and input constraints are ubiquitous in control system design. One recently developed tool to deal with these constraints is control barrier functions (CBF) which transform state constraints into conditions in the input space. CBF-based controller design thus incorporates both the CBF conditions and input constraints in a quadratic program. However, the CBF-based controller is well-defined only if the CBF conditions are compatible. In the case of perturbed systems, robust compatibility is of relevance. In this work, we propose an algorithmic solution to verify or falsify the (robust) compatibility of given CBFs a priori. Leveraging the Lipschitz properties of the CBF conditions, a grid sampling and refinement method with theoretical analysis and guarantees is proposed.