CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECT
For optimal stabilization of an autonomous linear system of differential equations with aftereffect and impulse controls, the formulation of the problem in the functional state space is used. For a system with aftereffect, approximating systems of ordinary differential equations proposed by S.N. Shi...
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2023-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/693 |
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| author | Yuri F. Dolgii |
| author_facet | Yuri F. Dolgii |
| author_sort | Yuri F. Dolgii |
| collection | DOAJ |
| description | For optimal stabilization of an autonomous linear system of differential equations with aftereffect and impulse controls, the formulation of the problem in the functional state space is used. For a system with aftereffect, approximating systems of ordinary differential equations proposed by S.N. Shimanov and J. Hale are used. A method for constructing approximations for optimal stabilizing control of an autonomous linear system with aftereffect and impulse controls is proposed. Matrix Riccati equations are used to find approximating controls. |
| format | Article |
| id | doaj-art-07e09b05e19a41df8e55b4193f0fac47 |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-07e09b05e19a41df8e55b4193f0fac472025-08-20T03:16:01ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522023-12-019210.15826/umj.2023.2.006195CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECTYuri F. Dolgii0Ural Federal University, 19 Mira str., Ekaterinburg, 620002For optimal stabilization of an autonomous linear system of differential equations with aftereffect and impulse controls, the formulation of the problem in the functional state space is used. For a system with aftereffect, approximating systems of ordinary differential equations proposed by S.N. Shimanov and J. Hale are used. A method for constructing approximations for optimal stabilizing control of an autonomous linear system with aftereffect and impulse controls is proposed. Matrix Riccati equations are used to find approximating controls.https://umjuran.ru/index.php/umj/article/view/693differential equation with aftereffect, canonical approximation, optimal stabilization, impulse control |
| spellingShingle | Yuri F. Dolgii CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECT Ural Mathematical Journal differential equation with aftereffect, canonical approximation, optimal stabilization, impulse control |
| title | CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECT |
| title_full | CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECT |
| title_fullStr | CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECT |
| title_full_unstemmed | CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECT |
| title_short | CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECT |
| title_sort | canonical approximations in impulse stabilization for a system with aftereffect |
| topic | differential equation with aftereffect, canonical approximation, optimal stabilization, impulse control |
| url | https://umjuran.ru/index.php/umj/article/view/693 |
| work_keys_str_mv | AT yurifdolgii canonicalapproximationsinimpulsestabilizationforasystemwithaftereffect |