Unmatched Control Barrier Functions: Certainty Equivalence Adaptive Safety

This work applies universal adaptive control to control barrier functions to achieve safe control of dynamical systems with parametric model uncertainties. The proposed approach utilizes the certainty equivalence principle to methodically select a model-parameterized control barrier function and corresponding safety controller from an allowable set with instantaneous parameter estimates. While such a combination does not necessarily yield forward invariance without additional requirements on the barrier function, we show that safety can indeed be established by simply adjusting the adaptation gain online. Simulation results demonstrate the approach.