On the parametric dependence of the volume of integral funnels and their approximations
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Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
On the parametric dependence of the volume of integral funnels and their approximations
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| Автор |
Ushakov, V. N.
Ershov, A. A. |
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| Тематика |
CONTROL NONLINEAR SYSTEMS
DIFFERENTIAL INCLUSIONS DISCRETE APPROXIMATION PARAMETRIC DEPEDENCE REACHABLE SETS VOLUME OF INTEGRAL FUNNEL |
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| Описание |
We consider a nonlinear control system in a finite-dimensional Euclidean space and on a finite time interval, which depends on a parameter. Reachable sets and integral funnels of a differential inclusion corresponding to a control system containing a parameter are studied. When studying numerous problems of control theory and differential games, constructing their solutions and estimating errors, various theoretical approaches and associated computational methods are used. The problems mentioned above include, for example, various types of approach problems, the resolving constructions of which can be described quite simply in terms of reachable sets and integral funnels. In this paper, we study the dependence of reachable sets and integral funnels on a parameter: the degree of this dependence on a parameter is estimated under certain conditions on the control system. The degree of dependence of the integral funnels is investigated for the change in their volume with a change in the parameter. To estimate this dependence, systems of sets in the phase space are introduced that approximate the reachable sets and integral funnels on a given time interval corresponding to a finite partition of this interval. In this case, the degree of dependence of the approximating system of sets on the parameter is first estimated, and then this estimate is used in estimating the dependence of the volume of the integral funnel of the differential inclusion on the parameter. This approach is natural and especially useful in the study of specific applied control problems, in solving which, in the end, one has to deal not with ideal reachable sets and integral funnels, but with their approximations corresponding to a discrete representation of the time interval. © 2022 Udmurt State University. All rights reserved.
Ministry of Education and Science of the Russian Federation, Minobrnauka, (075–02–2022–874) Funding. The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075–02–2022–874). |
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| Дата |
2024-04-08T11:07:54Z
2024-04-08T11:07:54Z 2022 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Ушаков, ВН & Ершов, АА 2022, 'О ПАРАМЕТРИЧЕСКОЙ ЗАВИСИМОСТИ ОБЪЕМА ИНТЕГРАЛЬНЫХ ВОРОНОК И ИХ АППРОКСИМАЦИЙ', Вестник Удмуртского университета. Математика. Механика. Компьютерные науки, Том. 32, № 3, стр. 447-462. https://doi.org/10.35634/vm220307
Ушаков, В. Н., & Ершов, А. А. (2022). О ПАРАМЕТРИЧЕСКОЙ ЗАВИСИМОСТИ ОБЪЕМА ИНТЕГРАЛЬНЫХ ВОРОНОК И ИХ АППРОКСИМАЦИЙ. Вестник Удмуртского университета. Математика. Механика. Компьютерные науки, 32(3), 447-462. https://doi.org/10.35634/vm220307 1994-9197 Final All Open Access; Bronze Open Access https://www.mathnet.ru/php/getFT.phtml?jrnid=vuu&paperid=820&what=fullt&option_lang=eng https://www.mathnet.ru/php/getFT.phtml?jrnid=vuu&paperid=820&what=fullt&option_lang=eng http://elar.urfu.ru/handle/10995/131536 49492763 10.35634/vm220307 85142906973 000916470800007 |
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| Язык |
ru
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Udmurt State University
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| Источник |
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki
Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Nauki |
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