# Data-Driven Input-Output Control Barrier Functions

arXiv: https://arxiv.org/abs/2502.17688 · HTML: https://mlsanity.com/paper/2502.17688/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2025.

## Built on by (most cited first, 2 of 2)

- [Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes](https://mlsanity.com/paper/2504.01007/) (2025)
- [Safety-Critical Contextual Control via Online Riemannian Optimization with World Models](https://mlsanity.com/paper/2604.19639/) (2026)

## Abstract (arXiv)

Control Barrier Functions (CBFs) offer a framework for ensuring set invariance and designing constrained control laws. However, crafting a valid CBF relies on system-specific assumptions and the availability of an accurate system model, underscoring the need for systematic data-driven synthesis methods. This paper introduces a data-driven approach to synthesizing a CBF for discrete-time LTI systems using only input-output measurements. The method begins by computing the maximal control invariant set using an input-output data-driven representation, eliminating the need for precise knowledge of the system's order and explicit state estimation. The proposed CBF is then systematically derived from this set, which can accommodate multiple input-output constraints. Furthermore, the proposed CBF is leveraged to develop a minimally invasive safety filter that ensures recursive feasibility with an adaptive decay rate. To improve clarity, we assume a noise-free dataset, though the method can be extended using data-driven reachability to capture noise effects and handle uncertainty. Finally, the effectiveness of the proposed method is demonstrated on an unknown time-delay system.