# Data-Driven Reachability Analysis Using Matrix Zonotopes

arXiv: https://arxiv.org/abs/2011.08472 · HTML: https://mlsanity.com/paper/2011.08472/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2020.

## Built on by (most cited first, 11 of 11)

- [Safe Reinforcement Learning Using Black-Box Reachability Analysis](https://mlsanity.com/paper/2204.07417/) (2022)
- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Safe LLM-Controlled Robots with Formal Guarantees via Reachability Analysis](https://mlsanity.com/paper/2503.03911/) (2025)
- [Safe Reinforcement Learning using Data-Driven Predictive Control](https://mlsanity.com/paper/2211.11027/) (2022)
- [Robust Data-Driven Predictive Control using Reachability Analysis](https://mlsanity.com/paper/2103.14110/) (2021)
- [GenCtrl -- A Formal Controllability Toolkit for Generative Models](https://mlsanity.com/paper/2601.05637/) (2026)
- [Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes](https://mlsanity.com/paper/2504.01007/) (2025)
- [Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemics](https://mlsanity.com/paper/2111.04704/) (2021)
- [Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets](https://mlsanity.com/paper/2210.01919/) (2022)
- [Learning from Uncertain Data: From Possible Worlds to Possible Models](https://mlsanity.com/paper/2405.18549/) (2024)
- [Matrix Zonotopic Attention: A Context-Adaptive Value Projection for Set Transformers](https://mlsanity.com/paper/2608.05472/) (2026)

## Abstract (arXiv)

In this paper, we propose a data-driven reachability analysis approach for unknown system dynamics. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analysis heavily relies on the existence of a suitable system model, which is often not directly available in practice. We instead propose a data-driven reachability analysis approach from noisy data. More specifically, we first provide an algorithm for over-approximating the reachable set of a linear time-invariant system using matrix zonotopes. Then we introduce an extension for Lipschitz nonlinear systems. We provide theoretical guarantees in both cases. Numerical examples show the potential and applicability of the introduced methods.