# Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes

arXiv: https://arxiv.org/abs/2504.01007 · HTML: https://mlsanity.com/paper/2504.01007/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Builds on (most cited first, 19 of 19)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Formal Synthesis of Stochastic Systems via Control Barrier Certificates](https://mlsanity.com/paper/1905.04585/) (2019)
- [Permissive Barrier Certificates for Safe Stabilization Using Sum-of-squares](https://mlsanity.com/paper/1802.08917/) (2018)
- [Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods](https://mlsanity.com/paper/1910.02500/) (2019)
- [TSSOS: A Moment-SOS hierarchy that exploits term sparsity](https://mlsanity.com/paper/1912.08899/) (2019)
- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Data-Driven Reachability Analysis with Christoffel Functions](https://mlsanity.com/paper/2104.13902/) (2021)
- [Data-driven verification and synthesis of stochastic systems via barrier certificates](https://mlsanity.com/paper/2111.10330/) (2021)
- [Data-Driven Reachability Analysis Using Matrix Zonotopes](https://mlsanity.com/paper/2011.08472/) (2020)
- [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023)
- [Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings](https://mlsanity.com/paper/2403.10497/) (2024)
- [On-The-Fly Control of Unknown Systems: From Side Information to Performance Guarantees through Reachability](https://mlsanity.com/paper/2011.05524/) (2020)
- [Data-driven and Model-based Verification: a Bayesian Identification Approach](https://mlsanity.com/paper/1509.03347/) (2015)
- [Enhancing Data-Driven Reachability Analysis using Temporal Logic Side Information](https://mlsanity.com/paper/2109.07121/) (2021)
- [Fine-Tuned Convex Approximations of Probabilistic Reachable Sets under Data-driven Uncertainties](https://mlsanity.com/paper/2303.01549/) (2023)
- [Data-Driven Input-Output Control Barrier Functions](https://mlsanity.com/paper/2502.17688/) (2025)
- [Data-Driven Robust Backward Reachable Sets for Set-Theoretic Model Predictive Control](https://mlsanity.com/paper/2303.04749/) (2023)
- [Robust Data-Driven Tube-Based Zonotopic Predictive Control with Closed-Loop Guarantees](https://mlsanity.com/paper/2409.14366/) (2024)

## Built on by (most cited first, 1 of 1)

- [Safe Multi-Robot Coordination via VLM-LLM Reasoning and Reachability Analysis](https://mlsanity.com/paper/2609.27816/) (2026)

## Abstract (arXiv)

Ensuring safety in cyber-physical systems (CPSs) is a critical challenge, especially when system models are difficult to obtain or cannot be fully trusted due to uncertainty, modeling errors, or environmental disturbances. Traditional model-based approaches rely on precise system dynamics, which may not be available in real-world scenarios. To address this, we propose a data-driven safety verification framework that leverages matrix zonotopes and barrier certificates to verify system safety directly from noisy data. Instead of trusting a single unreliable model, we construct a set of models that capture all possible system dynamics that align with the observed data, ensuring that the true system model is always contained within this set. This model set is compactly represented using matrix zonotopes, enabling efficient computation and propagation of uncertainty. By integrating this representation into a barrier certificate framework, we establish rigorous safety guarantees without requiring an explicit system model. Numerical experiments demonstrate the effectiveness of our approach in verifying safety for dynamical systems with unknown models, showcasing its potential for real-world CPS applications.