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

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.