Unmatched Control Barrier Functions: Certainty Equivalence Adaptive Safety

This work applies universal adaptive control to control barrier functions to achieve forward invariance of a safe set despite unmatched parametric uncertainties in a dynamical model. 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 adaption 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. As a result, this work represents the first adaptive safety approach that successfully employs the certainty equivalence principle without sacrificing safety guarantees.