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Название: Asymptotic Expansion of a Solution for One Singularly Perturbed Optimal Control Problem in Rn with a Convex Integral Quality Index
Авторы: Shaburov, A. A.
Дата публикации: 2017
Издатель: N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences
Ural Federal University named after the first President of Russia B.N. Yeltsin
Библиографическое описание: Shaburov A. A. Asymptotic Expansion of a Solution for One Singularly Perturbed Optimal Control Problem in Rn with a Convex Integral Quality Index / A. A. Shaburov. — DOI 10.15826/umj.2017.1.005. — Text : electronic // Ural Mathematical Journal. — 2017. — Volume 3. — № 1. — P. 68-75.
Аннотация: The paper deals with the problem of optimal control with a convex integral quality index for a linear steady-state control system in the class of piecewise continuous controls with a smooth control constraints. In a general case, for solving such a problem, the Pontryagin maximum principle is applied as the necessary and sufficient optimum condition. In this work, we deduce an equation to which an initial vector of the conjugate system satisfies. Then, this equation is extended to the optimal control problem with the convex integral quality index for a linear system with a fast and slow variables. It is shown that the solution of the corresponding equation as ε→0 tends to the solution of an equation corresponding to the limit problem. The results received are applied to study of the problem which describes the motion of a material point in Rn for a fixed period of time. The asymptotics of the initial vector of the conjugate system that defines the type of optimal control is built. It is shown that the asymptotics is a power series of expansion.
Ключевые слова: OPTIMAL CONTROL
SINGULARLY PERTURBED PROBLEMS
ASYMPTOTIC EXPANSION
SMALL PARAMETER
URI: http://elar.urfu.ru/handle/10995/93132
Условия доступа: Creative Commons Attribution License
Текст лицензии: https://creativecommons.org/licenses/by/4.0/
ISSN: 2414-3952
DOI: 10.15826/umj.2017.1.005
Сведения о поддержке: The author is very grateful to Prof. Alexey R.Danilin for the formulation of the problem and constant attention to the work.
Источники: Ural Mathematical Journal. 2017. Volume 3. № 1
Располагается в коллекциях:Ural Mathematical Journal

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