Email this article On the possibility of obtaining the optimal order of accuracy when restoring the impact by the dynamic method
- Authors: Vdovin A.Y.1, Rubleva S.S.1
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Affiliations:
- Ural State Forestry University
- Issue: Vol 25, No 130 (2020)
- Pages: 147-155
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/295073
- DOI: https://doi.org/10.20310/2686-9667-2020-25-130-147-155
- ID: 295073
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Abstract
Osipov and A. V. Kryazhimsky proposed a method of dynamic regulation to restore an unknown effect in a controlled model. In the framework of this approach, in the present work we study the property of another method based on the use of the implicit Euler method for the problem of numerical differentiation. The choice of the parameters of the method is indicated, which makes it possible to increase its efficiency, reduce the noise level of the approximate solution, and obtain the optimal order of accuracy in the metric L(T) ; equal to 1 2 .
About the authors
Andrey Yu. Vdovin
Ural State Forestry University
Email: vdovinau@m.usfeu.ru
Candidate of Physics and Mathematics, Head of the High Mathematics Department 37 Siberian tract St., Yekaterinburg 620100, Russian Federation
Svetlana S. Rubleva
Ural State Forestry University
Email: rublevass@m.usfeu.ru
Candidate of Physics and Mathematics, Associate Professor of of the High Mathematics Department 37 Siberian tract St., Yekaterinburg 620100, Russian Federation
References
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- Yu.S. Osipov, A.V. Kryazhimskii, Inverse Problems for Ordinary Differential Equations: Dynamical Solutions, Gordon and Breach, London, 1995.
- Н. Н. Красовский, Управление динамической системой. Задача о минимуме гарантированного результата, Наука, М., 1985.
- А.Ю. Вдовин, С.С. Рублева, “О гарантированной точности процедуры динамического восстановления управления с ограниченной вариацией, зависящей от него линейно”, Математические заметки, 87:3 (2010), 337-358.
- Д.В. Беклемишев, Дополнительные главы линейной алгебры, Наука, М., 1983.
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