Optimal control with impulsive component for systems described by implicit parabolic operator differential equations

We study the problem of optimal control with impulsive component for systems described by abstract Sobolev-type differential equations with unbounded operator coefficients in Hilbert spaces. The operator coefficient of the time derivative may be noninvertible. The main assumption is a restriction imposed on the resolvent of the characteristic operator pencil in a certain right half plane. Applications to Sobolevtype partial differential equations are discussed.