  This paper addresses the problem of safety-critical control for non-affine
control systems. It has been shown that optimizing quadratic costs subject to
state and control constraints can be sub-optimally reduced to a sequence of
quadratic programs (QPs) by using Control Barrier Functions (CBFs). Our
recently proposed High Order CBFs (HOCBFs) can accommodate constraints of
arbitrary relative degree. The main challenges in this approach are that it
requires affine control dynamics and the solution of the CBF-based QP is
sub-optimal since it is solved point-wise. To address these challenges, we
incorporate higher-order CBFs into neural ordinary differential equation-based
learning models as differentiable CBFs to guarantee safety for non-affine
control systems. The differentiable CBFs are trainable in terms of their
parameters, and thus, they can address the conservativeness of CBFs such that
the system state will not stay unnecessarily far away from safe set boundaries.
Moreover, the imitation learning model is capable of learning complex and
optimal control policies that are usually intractable online. We illustrate the
effectiveness of the proposed framework on LiDAR-based autonomous driving and
compare it with existing methods.
