# High Relative Degree Control Barrier Functions Under Input Constraints

arXiv: https://arxiv.org/abs/2106.10345 · HTML: https://mlsanity.com/paper/2106.10345/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2021.

## Built on by (most cited first, 3 of 3)

- [Exact Verification of ReLU Neural Control Barrier Functions](https://mlsanity.com/paper/2310.09360/) (2023)
- [Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation](https://mlsanity.com/paper/2410.16281/) (2024)
- [Pareto Control Barrier Function for Inner Safe Set Maximization Under Input Constraints](https://mlsanity.com/paper/2410.04260/) (2024)

## Abstract (arXiv)

This paper presents methodologies for ensuring forward invariance of sublevel sets of constraint functions with high-relative-degree with respect to the system dynamics and in the presence of input constraints. We show that such constraint functions can be converted into special Zeroing Control Barrier Functions (ZCBFs), which, by construction, generate sufficient conditions for rendering the state always inside a sublevel set of the constraint function in the presence of input constraints. We present a general form for one such ZCBF, as well as a special case applicable to a specific class of systems. We conclude with a comparison of system trajectories under the two ZCBFs developed and prior literature, and a case study for an asteroid observation problem using quadratic-program based controllers to enforce the ZCBF condition.