  We study a version of the stochastic control problem of minimizing the sum of
running and controlling costs, where control opportunities are restricted to
independent Poisson arrival times. Under a general setting driven by a general
L\'evy process, we show the optimality of a periodic barrier strategy, which
moves the process upward to the barrier whenever it is observed to be below it.
The convergence of the optimal solutions to those in the continuous-observation
case is also shown.
