ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD
The time-optimal problem for the controllable equation of heat conductivity in a rod is considered. By means of the Fourier expansion, the problem reduced to a countable system of one-dimensional control systems with a combined constraint joining control parameters in one relation. In order to impro...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
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
2019-07-01
|
| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/162 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850056428875677696 |
|---|---|
| author | Abdulla A. Azamov Jasurbek A. Bakhramov Odiljon S. Akhmedov |
| author_facet | Abdulla A. Azamov Jasurbek A. Bakhramov Odiljon S. Akhmedov |
| author_sort | Abdulla A. Azamov |
| collection | DOAJ |
| description | The time-optimal problem for the controllable equation of heat conductivity in a rod is considered. By means of the Fourier expansion, the problem reduced to a countable system of one-dimensional control systems with a combined constraint joining control parameters in one relation. In order to improve the time of a suboptimal control constructed by F.L. Chernous'ko, a method of grouping coupled terms of the Fourier expansion of a control function is applied, and a synthesis of the improved suboptimal control is obtained in an explicit form. |
| format | Article |
| id | doaj-art-c5a39042e06a4eb598e8f0945e2c47c8 |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2019-07-01 |
| 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-c5a39042e06a4eb598e8f0945e2c47c82025-08-20T02:51:42ZengUral 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 Journal2414-39522019-07-015110.15826/umj.2019.1.00275ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A RODAbdulla A. Azamov0Jasurbek A. Bakhramov1Odiljon S. Akhmedov2Institute of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Durmon yuli st., 29 Tashkent, 100125Institute of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Durmon yuli st., 29 Tashkent, 100125Institute of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Durmon yuli st., 29 Tashkent, 100125The time-optimal problem for the controllable equation of heat conductivity in a rod is considered. By means of the Fourier expansion, the problem reduced to a countable system of one-dimensional control systems with a combined constraint joining control parameters in one relation. In order to improve the time of a suboptimal control constructed by F.L. Chernous'ko, a method of grouping coupled terms of the Fourier expansion of a control function is applied, and a synthesis of the improved suboptimal control is obtained in an explicit form.https://umjuran.ru/index.php/umj/article/view/162Heat equation, Time-optimal problem, Pontryagin maximum principle, Suboptimal control, Synthesis of control |
| spellingShingle | Abdulla A. Azamov Jasurbek A. Bakhramov Odiljon S. Akhmedov ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD Ural Mathematical Journal Heat equation, Time-optimal problem, Pontryagin maximum principle, Suboptimal control, Synthesis of control |
| title | ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD |
| title_full | ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD |
| title_fullStr | ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD |
| title_full_unstemmed | ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD |
| title_short | ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD |
| title_sort | on the chernous ko time optimal problem for the equation of heat conductivity in a rod |
| topic | Heat equation, Time-optimal problem, Pontryagin maximum principle, Suboptimal control, Synthesis of control |
| url | https://umjuran.ru/index.php/umj/article/view/162 |
| work_keys_str_mv | AT abdullaaazamov onthechernouskotimeoptimalproblemfortheequationofheatconductivityinarod AT jasurbekabakhramov onthechernouskotimeoptimalproblemfortheequationofheatconductivityinarod AT odiljonsakhmedov onthechernouskotimeoptimalproblemfortheequationofheatconductivityinarod |