Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory
In the present article, we consider a von Kárman equation with long memory. The goal is to study a quadratic cost minimax optimal control problems for the control system governed by the equation. First, we show that the solution map is continuous under a weak assumption on the data. Then, we formula...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/1859736 |
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| _version_ | 1832566021385355264 |
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| author | Jin-soo Hwang |
| author_facet | Jin-soo Hwang |
| author_sort | Jin-soo Hwang |
| collection | DOAJ |
| description | In the present article, we consider a von Kárman equation with long memory. The goal is to study a quadratic cost minimax optimal control problems for the control system governed by the equation. First, we show that the solution map is continuous under a weak assumption on the data. Then, we formulate the minimax optimal control problem. We show the first and twice Fréchet differentiabilities of the nonlinear solution map from a bilinear input term to the weak solution of the equation. With the Fréchet differentiabilities of the control to solution mapping, we prove the uniqueness and existence of an optimal pair and find its necessary optimality condition. |
| format | Article |
| id | doaj-art-c6a6804c557047eda9d6b67b6f057d89 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-c6a6804c557047eda9d6b67b6f057d892025-02-03T01:05:21ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/18597361859736Bilinear Minimax Optimal Control Problems for a von Kárman System with Long MemoryJin-soo Hwang0Department of Mathematics Education, College of Education, Daegu University, Jillyang, Gyeongsan, Gyeongbuk, Republic of KoreaIn the present article, we consider a von Kárman equation with long memory. The goal is to study a quadratic cost minimax optimal control problems for the control system governed by the equation. First, we show that the solution map is continuous under a weak assumption on the data. Then, we formulate the minimax optimal control problem. We show the first and twice Fréchet differentiabilities of the nonlinear solution map from a bilinear input term to the weak solution of the equation. With the Fréchet differentiabilities of the control to solution mapping, we prove the uniqueness and existence of an optimal pair and find its necessary optimality condition.http://dx.doi.org/10.1155/2020/1859736 |
| spellingShingle | Jin-soo Hwang Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory Journal of Function Spaces |
| title | Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory |
| title_full | Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory |
| title_fullStr | Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory |
| title_full_unstemmed | Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory |
| title_short | Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory |
| title_sort | bilinear minimax optimal control problems for a von karman system with long memory |
| url | http://dx.doi.org/10.1155/2020/1859736 |
| work_keys_str_mv | AT jinsoohwang bilinearminimaxoptimalcontrolproblemsforavonkarmansystemwithlongmemory |