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Название: BILINEAR INTERPOLATION OF PROGRAM CONTROL IN APPROACH PROBLEM
Авторы: Ershov, A. A.
Дата публикации: 2023
Издатель: Institute of Mathematics with Computing Centre
Библиографическое описание: 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
Аннотация: 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.
Ключевые слова: APPROACH PROBLEM
BILINEAR INTERPOLATION
CONTROLLED SYSTEM
UNKNOWN CONSTANT PARAMETER
URI: http://elar.urfu.ru/handle/10995/130757
Условия доступа: info:eu-repo/semantics/openAccess
Идентификатор SCOPUS: 85169585616
Идентификатор WOS: 001057520500003
Идентификатор PURE: 44660050
ISSN: 2304-0122
DOI: 10.13108/2023-15-3-41
Сведения о поддержке: 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/.
Карточка проекта РНФ: 19-11-00105
Располагается в коллекциях:Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC

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