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This paper considers a scenario in which a secondary user (SU) opportunistically accesses a channel allocated to some primary network (PN) that switches between idle and active states in a time-slotted manner. At the beginning of each time slot, SU can choose to stay idle or to carry out spectrum sensing to detect the state of PN. If PN is detected to be idle, SU can carry out data transmission. Spectrum sensing consumes time and energy and introduces false alarms and mis-detections. The objective is to dynamically decide, for each time slot, whether SU should stay idle or carry out sensing, and if so, for how long, to maximize the expected reward. We formulate this as a partially observable Markov decision process and prove important properties of the optimal control policies. Heuristic control policies with low complexity and good performance are also proposed. Numerical results show the significant performance gain of our dynamic control approach for opportunistic spectrum access.