# Control Barrier Functions for Stochastic Systems and Safety-critical Control Designs

arXiv: https://arxiv.org/abs/2209.08728 · HTML: https://mlsanity.com/paper/2209.08728/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2022.

## Built on by (most cited first, 4 of 4)

- [CBF-LLM: Safe Control for LLM Alignment](https://mlsanity.com/paper/2408.15625/) (2024)
- [Myopically Verifiable Probabilistic Certificates for Safe Control and Learning](https://mlsanity.com/paper/2404.16883/) (2024)
- [Set Invariance with Probability One for Controlled Diffusion: Score-based Approach](https://mlsanity.com/paper/2507.22385/) (2025)
- [Control Barrier Function for Aligning Large Language Models](https://mlsanity.com/paper/2511.03121/) (2025)

## Abstract (arXiv)

In recent years, the analysis of a control barrier function has received considerable attention because it is helpful for the safety-critical control required in many control application problems. While the extension of the analysis to a stochastic system studied by many researchers, it remains a challenging issue. In this paper, we consider sufficient conditions for reciprocal and zeroing control barrier functions ensuring safety with probability one and design a control law using the functions. Then, we propose another version of a stochastic zeroing control barrier function to evaluate a probability of a sample path staying in a safe set and confirm the convergence of a specific expectation related to the attractiveness of a safe set. We also show a way of deisgning a safety-critical control law based on our stochastic zeroing control barrier function. Finally, we confirm the validity of the proposed control design and the analysis using the control barrier functions via simple examples with their numerical simulation.