Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays
Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient co...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2016-06-01
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| Series: | Archives of Control Sciences |
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| Online Access: | http://www.degruyter.com/view/j/acsc.2016.26.issue-2/acsc-2016-0011/acsc-2016-0011.xml?format=INT |
| _version_ | 1817989837769146368 |
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| author | Kowalewski Adam |
| author_facet | Kowalewski Adam |
| author_sort | Kowalewski Adam |
| collection | DOAJ |
| description | Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic equation with the Neumann boundary condition involving multiple time delays are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic cost function with pointwise observation of the state and constrained control are derived. |
| first_indexed | 2024-04-14T00:51:19Z |
| format | Article |
| id | doaj.art-ff2750f6c0954d96933ac9ce36887035 |
| institution | Directory Open Access Journal |
| issn | 2300-2611 |
| language | English |
| last_indexed | 2024-04-14T00:51:19Z |
| publishDate | 2016-06-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Control Sciences |
| spelling | doaj.art-ff2750f6c0954d96933ac9ce368870352022-12-22T02:21:47ZengPolish Academy of SciencesArchives of Control Sciences2300-26112016-06-0126218919710.1515/acsc-2016-0011acsc-2016-0011Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delaysKowalewski Adam0AGH University of Science and Technology, Institute of Automatics and Biomedical Engineering, 30-059 Cracow, al. Mickiewicza 30, PolandVarious optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic equation with the Neumann boundary condition involving multiple time delays are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic cost function with pointwise observation of the state and constrained control are derived.http://www.degruyter.com/view/j/acsc.2016.26.issue-2/acsc-2016-0011/acsc-2016-0011.xml?format=INTdistributed controlparabolic systemtime delayspointwise observation |
| spellingShingle | Kowalewski Adam Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays Archives of Control Sciences distributed control parabolic system time delays pointwise observation |
| title | Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays |
| title_full | Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays |
| title_fullStr | Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays |
| title_full_unstemmed | Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays |
| title_short | Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays |
| title_sort | pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays |
| topic | distributed control parabolic system time delays pointwise observation |
| url | http://www.degruyter.com/view/j/acsc.2016.26.issue-2/acsc-2016-0011/acsc-2016-0011.xml?format=INT |
| work_keys_str_mv | AT kowalewskiadam pointwiseobservationofthestategivenbyparabolicsystemwithboundaryconditioninvolvingmultipletimedelays |