  It has been shown that optimizing quadratic costs while stabilizing affine
control systems to desired (sets of) states subject to state and control
constraints can be reduced to a sequence of Quadratic Programs (QPs) by using
Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In this
paper, we employ machine learning techniques to ensure the feasibility of these
QPs, which is a challenging problem, especially for high relative degree
constraints where High Order CBFs (HOCBFs) are required. To this end, we
propose a sampling-based learning approach to learn a new feasibility
constraint for CBFs; this constraint is then enforced by another HOCBF added to
the QPs. The accuracy of the learned feasibility constraint is recursively
improved by a recurrent training algorithm. We demonstrate the advantages of
the proposed learning approach to constrained optimal control problems with
specific focus on a robot control problem and on autonomous driving in an
unknown environment.
