  This work applies universal adaptive control to control barrier functions to
achieve forward invariance of a safe set despite the presence of unmatched
parametric uncertainties. The approach combines two ideas. The first is to
construct a family of control barrier functions that ensures the system is safe
for all possible models. The second is to use online parameter adaptation to
methodically select a control barrier function and corresponding safety
controller from the allowable set. While such a combination does not
necessarily yield forward invariance without additional requirements on the
barrier function, we show that such invariance can be established by simply
adjusting the adaptation gain online. It is also shown that the developed
method is applicable to systems with safety constraints that have a relative
degree greater than one. This work thus represents the first adaptive safety
approach that successfully employs the certainty equivalence principle for
general state constraints without sacrificing safety guarantees.
