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Bogolyubov's theorem under constraints generated by a controlled second-order evolution system

Авторы: Tolstonogov A.A.

Журнал: Izvestiya Mathematics

Том: 67

Номер: 5

Год: 2003

Отчётный год: 2003

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DOI: 10.1070/IM2003v067n05ABEH000456

Аннотация: We prove an analogue of Bogolyubov's theorem with constraints in the form of a controlled second-order evolution system. The main assertion of this theorem deals with relations between the values of an integral functional that is non-convex with respect to control on the solutions of a controlled system with non-convex constraints on the control and the values of the functional convexified with respect to control on the solutions of a controlled system with convexified constraints. This theorem also establishes relations between the solutions of non-convex and convexified controlled systems. We apply the theorem to the problem of minimizing a non-convex integral functional on the solutions of a non-convex controlled system. We consider in detail an example of a non-linear hyperbolic system.

Индексируется WOS: Q2

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Да

Индексируется ВАК: Нет

Индексируется CORE: Нет

Публикация в печати: 0