Optimal processes governed by integral equation: equations with unilateral constraint (Q2640127)

The author considers optimal control problems for systems governed by integral equations with unilateral constraint. The investigation is based on the concepts of a ``relaxed control'' and a ``relaxed admissible pair''. The existence of optimal relaxed admissible pairs is shown for the class of problems under consideration. A necessary condition is derived for a relaxed admissible pair to be optimal. The author presents a certain subclass of linear problems where an optimal relaxed control reduces to a bounded measurable function. If for this special class of problems the values of control functions are selected from a convex polyhedron, then the optimal controls take their values in the vertices of this polyhedron.