  In this paper, we present a framework for online parameter estimation and
uncertainty quantification in the context of adaptive safety-critical control.
The key insight enabling our approach is that the parameter estimate generated
by the continuous-time recursive least squares (RLS) algorithm at any point in
time is an affine transformation of the initial parameter estimate. This
property allows for parameterizing such estimates using objects that are closed
under affine transformation, such as zonotopes, and enables the efficient
propagation of such set-based estimates as time progresses. We illustrate how
such an approach facilitates the synthesis of safety-critical controllers for
systems with parametric uncertainty and additive disturbances using control
barrier functions, and demonstrate the utility of our approach through
illustrative examples.
