Evolution equations determined by operator valued measures and optimal control

In this paper we consider a general class of systems determined by operator valued measures. Briefly we review some recent results on optimal control with controls being vector measures. Then we consider problems of structural controls where the operator valued measures are considered as the controls. We prove existence of optimal controls for linear and semilinear problems. The basic results are illustrated by several examples from systems governed by partial differential equations of hyperbolic as well as parabolic types containing coefficients which are vector measures.