Consideration was given to the class of optimal control problems for the differential systems with unbounded linear control and, in particular, the classes of problems for the bilinear systems. Such problems are distinguished for the lack of minimum (maximum) on the ordinary class of permissible processes (continuous trajectories, sectionally continuous controls) and for reaching it on some closure of this class including processes with discontinuous trajectories. A direct iterative method for optimization of controls was developed.
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