BILINEAR INTERPOLATION OF PROGRAM CONTROL IN APPROACH PROBLEM
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
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BILINEAR INTERPOLATION OF PROGRAM CONTROL IN APPROACH PROBLEM
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| Автор |
Ershov, A. A.
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| Тематика |
APPROACH PROBLEM
BILINEAR INTERPOLATION CONTROLLED SYSTEM UNKNOWN CONSTANT PARAMETER |
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| Описание |
We consider a controlled system involving a constant two-dimensional vector parameter, the approximate value of which is reported to the controlling person only at the moment of the start of movement. Apriori only the set of possible values of these unknown parameter is given. For this controlled system we pose the problem on approaching the target set at a given time. At the same time, we suppose that the controlling person has no the ability to carry out cumbersome calculations in real time associated with the construction of such resolving structures as reachability sets and integral funnels. Therefore, to solve this problem, it is proposed to calculate in advance several “node” resolving controls for parameter values, which are nodes of a grid covering a set of possible parameter values. If at the moment of the beginning of the movement, the parameter value turns out not coincide with any of the grid nodes, it is proposed to calculate the software control by using linear interpolation formulas. However, this procedure can be effective only if a linear combination of controls corresponding to the same “guide” is used in the terminology of the N.N. Krasovsky extreme aiming method. For the possibility of effective use of linear interpolation, it is proposed to build four “node” resolving controls for each grid node and, in addition, to use the method of dividing the control into the main and compensating ones. Due to the application of the latter method, the computed solvability set turns out to be somewhat less than the actual one, but the accuracy of translating the state of the system to the target set increases. A nonlinear generalization of the Zermelo navigation problem is considered as an example. © Ershov A.A. 2023.
Russian Science Foundation, RSF: 19-11-00105 A.A. Ershov, Bilinear interpolation of program control in approach problem. © Ershov A.A. 2023. The research is supported by Russian Science Foundation, grant no. https://rscf.ru/en/project/19-11-00105/. Submitted August 23, 2022. The research is supported by Russian Science Foundation, grant no. 19-11-00105, https://rscf.ru/en/project/19-11-00105/. |
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| Дата |
2024-04-05T16:32:11Z
2024-04-05T16:32:11Z 2023 |
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Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Ershov, AA 2023, 'BILINEAR INTERPOLATION OF PROGRAM CONTROL IN APPROACH PROBLEM', Ufa Mathematical Journal, Том. 15, № 3, стр. 41-53. https://doi.org/10.13108/2023-15-3-41
Ershov, A. A. (2023). BILINEAR INTERPOLATION OF PROGRAM CONTROL IN APPROACH PROBLEM. Ufa Mathematical Journal, 15(3), 41-53. https://doi.org/10.13108/2023-15-3-41 2304-0122 Final All Open Access, Bronze https://www.scopus.com/inward/record.uri?eid=2-s2.0-85169585616&doi=10.13108%2f2023-15-3-41&partnerID=40&md5=993cf4b46e4db679dda5d5031edbced2 https://matem.anrb.ru/sites/default/files/files/vupe59/Ershov.pdf http://elar.urfu.ru/handle/10995/130757 10.13108/2023-15-3-41 85169585616 001057520500003 |
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| Язык |
en
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| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//19-11-00105
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Institute of Mathematics with Computing Centre
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| Источник |
Ufa Mathematical Journal
Ufa Mathematical Journal |
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