We consider a version of the stochastic control problem, in which control opportunities arrive only at the jump times of an independent Poisson process. We consider perpetual American options, optimal dividend problems, and inventory control problems, driven by a spectrally one-sided Levy process. In particular, we show that barrier-type strategies are optimal under suitable conditions. The optimal strategies and value functions are concisely written in terms of the scale functions. This talk is based on the joint work with A. Bensoussan and J.L. Perez.