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

TL;DR

This paper introduces a novel model-free method for designing control barrier functions (CBFs) that ensures safety in nonlinear systems without requiring system models, by leveraging funnel control techniques.

Contribution

It develops a model-free CBF-based control design approach that uses output measurements and funnel control, bridging the gap between safety guarantees and model-free reactive feedback.

Findings

Established a connection between zeroing CBFs and funnel control.

Demonstrated the approach with a numerical simulation.

Eliminated the need for system dynamics knowledge in CBF design.

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.