Optimal switching for alternating processes (Q1093614)

The author considers the optimal switching problem for a finite set of alternating general processes with a cost function in integral form. Admissible control is represented by a sequence of stopping times \(T_ n\) and a sequence of corresponding numbers of processes chosen at each \(T_ n\). The existence of the maximal element of a class of dynamic programming inequalities is shown by the method of impulsive control. This is used to obtain results on the existence of optimal control for general and cyclic switching problems.