  Approaches to keeping a dynamical system within state constraints typically
rely on a model-based safety condition to limit the control signals. In the
face of significant modeling uncertainty, the system can suffer from important
performance penalties due to the safety condition becoming overly conservative.
Machine learning can be employed to reduce the uncertainty around the system
dynamics, and allow for higher performance. In this article, we propose the
safe uncertainty learning principle, and argue that the learning must be
properly structured to preserve safety guarantees. For instance, robust safety
conditions are necessary, and they must be initialized with conservative
uncertainty bounds prior to learning. Also, the uncertainty bounds should only
be tightened if the collected data sufficiently capture the future system
behavior. To support the principle, two example problems are solved with
control barrier functions: a lane-change controller for an autonomous vehicle,
and an adaptive cruise controller. This work offers a way to evaluate if
machine learning preserves safety guarantees during the control of uncertain
dynamical systems. It also highlights challenging aspects of learning for
control.
