# Zero-Order Control Barrier Functions for Sampled-Data Systems with State and Input Dependent Safety Constraints

arXiv: https://arxiv.org/abs/2411.17079 · HTML: https://mlsanity.com/paper/2411.17079/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2024.

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

- [Safe Gradient Flow for Bilevel Optimization](https://mlsanity.com/paper/2501.16520/) (2025)
- [PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles](https://mlsanity.com/paper/2511.15522/) (2025)

## Abstract (arXiv)

We propose a novel zero-order control barrier function (ZOCBF) for sampled-data systems to ensure system safety. Our formulation generalizes conventional control barrier functions and straightforwardly handles safety constraints with high-relative degrees or those that explicitly depend on both system states and inputs. The proposed ZOCBF condition does not require any differentiation operation. Instead, it involves computing the difference of the ZOCBF values at two consecutive sampling instants. We propose three numerical approaches to enforce the ZOCBF condition, tailored to different problem settings and available computational resources. We demonstrate the effectiveness of our approach through a collision avoidance example and a rollover prevention example on uneven terrains.