  Correct-by-construction techniques, such as control barrier functions (CBFs),
can be used to guarantee closed-loop safety by acting as a supervisor of an
existing or legacy controller. However, supervisory-control intervention
typically compromises the performance of the closed-loop system. On the other
hand, machine learning has been used to synthesize controllers that inherit
good properties from a training dataset, though safety is typically not
guaranteed due to the difficulty of analyzing the associated neural network. In
this paper, supervised learning is combined with CBFs to synthesize controllers
that enjoy good performance with provable safety. A training set is generated
by trajectory optimization that incorporates the CBF constraint for an
interesting range of initial conditions of the truck model. A control policy is
obtained via supervised learning that maps a feature representing the initial
conditions to a parameterized desired trajectory. The learning-based controller
is used as the performance controller and a CBF-based supervisory controller
guarantees safety. A case study of lane keeping for articulated trucks shows
that the controller trained by supervised learning inherits the good
performance of the training set and rarely requires intervention by the CBF
supervisor
