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

Abstract

Control barrier functions guarantee safety but require accurate system models; parametric uncertainty invalidates these guarantees. Existing robust methods maintain safety via worst-case bounds at the cost of performance, while modular learning schemes decouple estimation from safety and risk constraint violations during transients. This paper presents the composite adaptive control barrier function (CaCBF) algorithm for nonlinear control-affine systems with linear parametric uncertainty. The adaptation law is derived from a composite energy function integrating a logarithmic safety barrier, a control Lyapunov function, and a parameter-error term, creating a direct coupling between estimation accuracy and the safety margin. We prove three main results: (i) the safe set is forward invariant for all bounded parameters, without requiring persistence of excitation; (ii) the safety guarantee is robust to bounded errors in the state-derivative measurement; and (iii) all closed-loop signals are uniformly ultimately bounded. We further prove that the CaCBF admissible control set always contains the robust counterpart as a subset. Simulations of adaptive cruise control, an omnidirectional robot, and a planar drone traversing a narrow gate confirm that CaCBF recovers the performance margin surrendered by robust methods while maintaining strict safety throughout.