# Data-Driven Permissible Safe Control with Barrier Certificates

arXiv: https://arxiv.org/abs/2405.00136 · HTML: https://mlsanity.com/paper/2405.00136/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 30 Apr 2024.

## Builds on (most cited first, 12 of 12)

- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [On a Formal Model of Safe and Scalable Self-driving Cars](https://mlsanity.com/paper/1708.06374/) (2017)
- [Safety Certification for Stochastic Systems via Neural Barrier Functions](https://mlsanity.com/paper/2206.01463/) (2022)
- [Formal Synthesis of Stochastic Systems via Control Barrier Certificates](https://mlsanity.com/paper/1905.04585/) (2019)
- [A Barrier Function Approach to Finite-Time Stochastic System Verification and Control](https://mlsanity.com/paper/1909.05109/) (2019)
- [Safety Guarantees for Neural Network Dynamic Systems via Stochastic Barrier Functions](https://mlsanity.com/paper/2206.07811/) (2022)
- [Computing Probabilistic Controlled Invariant Sets](https://mlsanity.com/paper/1905.04117/) (2019)
- [Formal Verification of Unknown Dynamical Systems via Gaussian Process Regression](https://mlsanity.com/paper/2201.00655/) (2021)
- [Formal Abstraction of General Stochastic Systems via Noise Partitioning](https://mlsanity.com/paper/2309.10702/) (2023)
- [Piecewise Stochastic Barrier Functions](https://mlsanity.com/paper/2404.16986/) (2024)

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

- [Learning-Based Shielding for Safe Autonomy under Unknown Dynamics](https://mlsanity.com/paper/2410.07359/) (2024)
- [BarrierBench: Evaluating Large Language Models for Safety Verification in Dynamical Systems](https://mlsanity.com/paper/2511.09363/) (2025)
- [Kernel-Based Learning of Safety Barriers](https://mlsanity.com/paper/2601.12002/) (2026)

## Abstract (arXiv)

This paper introduces a method of identifying a maximal set of safe strategies from data for stochastic systems with unknown dynamics using barrier certificates. The first step is learning the dynamics of the system via Gaussian process (GP) regression and obtaining probabilistic errors for this estimate. Then, we develop an algorithm for constructing piecewise stochastic barrier functions to find a maximal permissible strategy set using the learned GP model, which is based on sequentially pruning the worst controls until a maximal set is identified. The permissible strategies are guaranteed to maintain probabilistic safety for the true system. This is especially important for learning-enabled systems, because a rich strategy space enables additional data collection and complex behaviors while remaining safe. Case studies on linear and nonlinear systems demonstrate that increasing the size of the dataset for learning the system grows the permissible strategy set.