Data-Driven Input-Output Control Barrier Functions

TL;DR

This paper presents a novel data-driven method for synthesizing Control Barrier Functions for discrete-time LTI systems using only input-output data, enabling safety guarantees without explicit system models.

Contribution

It introduces a systematic approach to derive CBFs directly from input-output measurements, bypassing the need for explicit system identification or state estimation.

Findings

Successfully synthesized CBFs for unknown systems

Developed a safety filter ensuring recursive feasibility

Validated method on a time-delay system

Abstract

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.