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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 8, pp. 1053–1065, August, 2009.
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Vlasenko, L.A., Samoilenko, A.M. Optimal control with impulsive component for systems described by implicit parabolic operator differential equations. Ukr Math J 61, 1250–1263 (2009). https://doi.org/10.1007/s11253-010-0274-1
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DOI: https://doi.org/10.1007/s11253-010-0274-1