  The controller of an input-affine system is determined through minimizing a
time-varying objective function, where stabilization is ensured via a Lyapunov
function decay condition as constraint. This constraint is incorporated into
the objective function via a barrier function. The time-varying minimum of the
resulting relaxed cost function is determined by a tracking system. This system
is constructed using derivatives up to second order of the relaxed cost
function and improves the existing approaches in time-varying optimization.
Under some mild assumptions, the tracking system yields a solution which is
feasible for all times, and it converges to the optimal solution of the relaxed
objective function in a user-defined fixed-time. The effectiveness of these
results in comparison to exponential convergence is demonstrated in a case
study.
