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Of concern is the optimal control problem for the Sobolev type higher order equation with relatively polynomially bounded operator pencil. The theorem of existence and uniqueness of strong solutions to the initial-final problem for abstract equation is proved. The sufficient conditions for optimal control existence and uniqueness of such solutions are found. We use the ideas and methods developed by G.A. Sviridyuk and his disciples.

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 ðàáîòå èññëåäîâàíà çàäà÷à îïòèìàëüíîãî óïðàâëåíèÿ äëÿ íåïîëíîãî óðàâíåíèÿ ñîáîëåâñêîãî òèïà âûñîêîãî ïîðÿäêà. Äîêàçàíà òåîðåìà ñóùåñòâîâàíèÿ è åäèíñòâåííîñòè ñèëüíîãî ðåøåíèÿ çàäà÷è Êîøè äëÿ äàííîãî óðàâíåíèÿ. Ïîëó÷åíû äîñòàòî÷íûå óñëîâèÿ ñóùåñòâîâàíèÿ è åäèíñòâåííîñòè îïòèìàëüíîãî óïðàâëåíèÿ òàêèìè ðåøåíèÿìè.  ðàáîòå èñïîëüçóþòñÿ èäåè è ìåòîäû, ðàçðàáîòàííûå Ã.À. Ñâèðèäþêîì è åãî ó÷åíèêàìè. Äîêàçàòåëüñòâî òåîðåìû î ñóùåñòâîâàíèè è åäèíñòâåííîñòè îïòèìàëüíîãî óïðàâëåíèÿ äëÿ èññëåäóåìîé çàäà÷è îïèðàåòñÿ íà òåîðèþ îïòèìàëüíîãî óïðàâëåíèÿ, ðàçâèòóþ â ðàáîòàõ AE.-Ë. Ëèîíñà.

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