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We study the problem of optimal control for a class of evolutionary parabolic functional-differential equations in Banach spaces. Sufficient conditions for the existence of an optimal pair are established. Note that the main problem of optimal control is considered up to the time of exit of the solution from the domain, which distinguishes the analyzed problem from the other investigations. [ABSTRACT FROM AUTHOR]

We consider the optimal control problem for systems with infinite memory whose models are described by functional-differential equations. We prove the theorem on existence, uniqueness, and continuity of solutions for a system of functional-differential equations in which the delay interval is infinitely large. Sufficient conditions for the existence of optimal controls in the optimal control problems for systems with infinite memory are obtained in terms of the right-hand sides of the equations of motion and the function of performance criterion. [ABSTRACT FROM AUTHOR]