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Continuity in the parameter of the minimum value of an integral functional over the solutions of an evolution control systems
Авторы: Tolstonogov A.A.
Журнал: Nonlinear Analysis: Theory, Methods & Applications
Том: 75
Номер: 12
Год: 2012
Отчётный год: 2012
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Аннотация: The problem of minimization of an integral functional with an integrand that is nonconvex with respect to the control is considered. We minimize our functional over the solution set of a nonlinear evolution control system with a time-dependent subdifferential operator in a Hilbert space. The control constraint is given by a nonconvex closed bounded set. The integrand, the control constraint, the initial conditions and the operators in the equation describing the control system all depend on a parameter. We consider, along with the original problem, the problem of minimizing an integral functional with an integrand convexified with respect to the control over the solution set of the same system, but now subject to the convexified control constraint. By a solution of the control system we mean a "trajectory-control'' pair. We prove that for each value of the parameter the convexified problem has a solution, which is the limit of a minimizing sequence of the original problem, and the minimum value of the functional of the convexified problem is a continuous function of the parameter.
Индексируется WOS: Q1
Индексируется Scopus: Нет
Индексируется УБС: Нет
Индексируется РИНЦ: Да
Индексируется ВАК: Нет
Индексируется CORE: Нет
Публикация в печати: 0
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