  Recent work has shown that stabilizing an affine control system to a desired
state while optimizing a quadratic cost 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 our
own recent work, we defined High Order CBFs (HOCBFs) for systems and
constraints with arbitrary relative degrees. In this paper, in order to
accommodate initial states that do not satisfy the state constraints and
constraints with arbitrary relative degree, we generalize HOCBFs to High Order
Control Lyapunov-Barrier Functions (HOCLBFs). We also show that the proposed
HOCLBFs can be used to guarantee the Boolean satisfaction of Signal Temporal
Logic (STL) formulae over the state of the system. We illustrate our approach
on a safety-critical optimal control problem (OCP) for a unicycle.
