  Safety in dynamical systems is commonly pursued using control barrier
functions (CBFs) which enforce safety-constraints over the entire duration of a
system's evolution. We propose a prescribed-time safety (PTSf) design which
enforces safety only for a finite time of interest to the user. While
traditional CBF designs would keep the system away from the barrier longer than
necessary, our PTSf design lets the system reach the barrier by the prescribed
time and obey the operator's intent thereafter. To emphasize the capability of
our design for safety constraints with high relative degrees, we focus our
exposition on a chain of integrators where the safety condition is defined for
the state furthest from the control input. In contrast to existing CBF-based
methods for high-relative degree constraints, our approach involves choosing
explicitly specified gains (instead of class $\mathcal{K}$ functions), and,
with the aid of backstepping, operates in the entirety of the original safe set
with no additional restriction on the initial conditions. With Quadratic
Programming (QP) being employed in the design, in addition to backstepping and
CBFs with a PTSf property, we refer to our design as a QP-backstepping PT-CBF
design. For illustration, we include a simulation for the double-integrator
system.
