Composite Adaptive Control Barrier Functions for Safety-Critical Systems with Parametric Uncertainty

TL;DR

This paper introduces the CaCBF algorithm, which ensures safety in nonlinear control systems with parametric uncertainty by combining adaptive laws with control barrier functions, without needing parameter convergence.

Contribution

The paper develops a novel composite adaptive control barrier function approach that guarantees safety and boundedness in uncertain systems without requiring parameter convergence.

Findings

CaCBF guarantees forward invariance of the safe set.

The method ensures boundedness of the closed-loop system.

Simulations demonstrate effectiveness in various control scenarios.

Abstract

Control barrier functions guarantee safety but typically require accurate system models. Parametric uncertainty invalidates these guarantees. Existing robust methods maintain safety via worst-case bounds, limiting performance, while modular learning schemes decouple estimation from safety, permitting state violations during training. This paper presents the composite adaptive control barrier function (CaCBF) algorithm for nonlinear control-affine systems subject to linear parametric uncertainty. We derive adaptation laws from a composite energy function comprising a logarithmic safety barrier, a control Lyapunov function, and a parameter error term. We prove that CaCBF guarantees the forward invariance of the safe set and the uniform boundedness of the closed-loop system. This safety guarantee holds without requiring parameter convergence. Simulations of adaptive cruise control, an omnidirectional robot, and a planar drone demonstrate the efficacy of the CaCBF algorithm.