Unmatched Control Barrier Functions: Certainty Equivalence Adaptive Safety

TL;DR

This paper introduces an adaptive control method using control barrier functions to ensure safety in systems with uncertainties, employing online parameter adaptation and certainty equivalence to maintain forward invariance of safe sets.

Contribution

It presents the first adaptive safety approach applying certainty equivalence to general state constraints without compromising safety guarantees.

Findings

Ensures safety despite unmatched parametric uncertainties.

Uses online adaptation gain adjustment for forward invariance.

Applicable to systems with safety constraints of relative degree greater than one.

Abstract

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.