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arXiv · 2505.17887

A model-free approach to control barrier functions using funnel control

Lukas Lanza·Johannes Köhler·Dario Dennstädt·Thomas Berger·Karl Worthmann
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Abstract

Control barrier functions (CBFs) are a popular approach to design feedback laws that achieve safety guarantees for nonlinear systems. The CBF-based controller design relies on the availability of a model to select feasible inputs from the set of CBF-based controls. In this paper, we develop a model-free approach to design CBF-based control laws, eliminating the need for knowledge of system dynamics or parameters. Specifically, we address safety requirements characterized by a time-varying distance to a reference trajectory in the output space and construct a CBF that depends only on the measured output. Utilizing this particular CBF, we determine a subset of CBF-based controls without relying on a model of the dynamics by using techniques from funnel control. The latter is a model-free high-gain adaptive control methodology, which achieves tracking guarantees via reactive feedback. In this paper, we discover and establish a connection between the modular controller synthesis via zeroing CBFs and model-free reactive feedback. The theoretical results are illustrated by a numerical simulation.

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Lukas Lanza, Johannes Köhler, Dario Dennstädt, Thomas Berger, Karl Worthmann. 2025-05-23. A model-free approach to control barrier functions using funnel control. https://arxiv.org/abs/2505.17887

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