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Proof of the maximum principle for a problem with state constraints by the v-change of time variableстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 11 ноября 2019 г.
- Авторы: Dmitruk A.V., Osmolovskii N.P.
- Журнал: Discrete and Continuous Dynamical Systems - Series B
- Том: 24
- Номер: 5
- Год издания: 2019
- Издательство: American Institute of Mathematical Sciences
- Местоположение издательства: United States
- Первая страница: 2189
- Последняя страница: 2204
- DOI: 10.3934/dcdsb.2019090
- Аннотация: We give a new proof of the maximum principle for optimal control problems with running state constraints. The proof uses the so-called method of v−change of the time variable introduced by Dubovitskii and Milyutin. In this method, the time t is considered as a new state variable satisfying the equation dt/dτ = v, where v(τ) ≥ 0 is a new control and τ a new time. Unlike the general v−change with an arbitrary v(τ), we use a piecewise constant v. Every such v−change reduces the original problem to a problem in a finite dimensional space, with a continuum number of inequality constrains corresponding to the state constraints. The stationarity conditions in every new problem, being written in terms of the original time t, give a weak* compact set of normalized tuples of Lagrange multipliers. The family of these compacta is centered and thus has a nonempty intersection. An arbitrary tuple of Lagrange multipliers belonging to the latter ensures the maximum principle.
- Добавил в систему: Дмитрук Андрей Венедиктович