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A new framework is developed for control of constrained nonlinear systemswith structured parametric uncertainties. Forward invariance of a safe set isachieved through online parameter adaptation and data-driven model estimation.The new adaptive data-driven safety paradigm is merged with a recent adaptivecontrol algorithm for systems nominally contracting in closed-loop. Thisunification is more general than other safety controllers as closed-loopcontraction does not require the system be invertible or in a particular form.Additionally, the approach is less expensive than nonlinear model predictivecontrol as it does not require a full desired trajectory, but rather only adesired terminal state. The approach is illustrated on the pitch dynamics of anaircraft with uncertain nonlinear aerodynamics.

Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version)