  This paper investigates the control barrier function (CBF) based
safety-critical control for continuous nonlinear control affine systems using
the more efficient online algorithms through time-varying optimization. The
idea lies in that when quadratic programming (QP) or other convex optimization
algorithms needed in the CBF-based method is not computation affordable, the
alternative suboptimal feasible solutions can be obtained more economically. By
using the barrier-based interior point method, the constrained CBF-QP problems
are converted into the unconstrained ones with suboptimal solutions tracked by
two continuous descent-based algorithms. Considering the lag effect of tracking
and exploiting the system information, the prediction method is added to the
algorithms which thereby achieves a exponential convergence rate to the
time-varying suboptimal solutions. The convergence and robustness of the
designed methods as well as the safety criteria of the algorithms are analyzed
theoretically. In the end, the effectiveness is illustrated by simulations on
the anti-swing and obstacle avoidance tasks.
