Approximate solution of the time-optimal problem involving delayстатья
Информация о цитировании статьи получена из
Scopus
Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
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Авторы:
Vasil’ev F.P.,
Ivanov R.P.
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Журнал:
USSR Computational Mathematics and Mathematical Physics
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Том:
10
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Номер:
5
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Год издания:
1970
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Первая страница:
74
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Последняя страница:
94
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Аннотация:
The time-optimal problem is considered below in a fairly general form (see problem (1.1)-(1.4), Section 1). For the investigation, auxiliary functions (see function M(c, t) and ρ(t) in Section 2) are introduced and their properties examined. It turns out that, given constraints on the phase coordinates, these functions can be discontinuous in t; it proves essential to know the nature of these discontinuities if we are to construct correctly, and investigate the convergence of, the algorithms for solving the time-optimal problems in question. Two methods for solving approximately the problem (1.1)-(1.4) are described and proved (Sections 3, 4), and their computational aspects are discussed (Section 5). Incidentally, a necessary and sufficient condition for controllability of the systems (1.1)-(1.3) is obtained in Section 2. Instead of listing all the papers in which aspects of time-optimal problems and controllability of linear systems are discussed, we refer the reader to the bibliographies in [1, 2]. The iterative methods described in the present paper for solving time-optimal problems are an extension of the methods described in [3, 4] (see also [2]), where very particular cases of problem (1.1)-(1.4) were discussed, with clamped ends and no constraints on the phase coordinates. © 1972.
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Добавил в систему:
Васильев Федор Павлович