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Variational stability of optimal control problems involving subdifferential operators

Авторы: Tolstonogov A.A.

Журнал: Sbornik Mathematics

Том: 202

Номер: 4

Год: 2011

Отчётный год: 2011

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Местоположение издательства:

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DOI: 10.1070/SM2011v202n04ABEH004157

Аннотация: This paper is concerned with the problem of minimizing an integral functional with control-nonconvex integrand over the class of solutions of a control system in a Hilbert space subject to a control constraint given by a phase-dependent multivalued map with closed nonconvex values. The integrand, the subdifferential operators, the perturbation term, the initial conditions and the control constraint all depend on a parameter. Along with this problem, the paper considers the problem of minimizing an integral functional with control-convexified integrand over the class of solutions of the original system, but now subject to a convexified control constraint. By a solution of a control system we mean a 'trajectory-control' pair. For each value of the parameter, the convexified problem is shown to have a solution, which is the limit of a minimizing sequence of the original problem, and the minimal value of the functional with the convexified integrand is a continuous function of the parameter. This property is commonly referred to as the variational stability of a minimization problem. An example of a control parabolic system with hysteresis and diffusion effects is considered.

Индексируется WOS: Q2

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Нет

Индексируется ВАК: Нет

Индексируется CORE: Нет

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