Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions
Two linear-quadratic problems are considered on the set of piecewise-constant controls. The first problem contains a discrete perturbation on the right side of the controlled system and uncertain parameters in a quadratic functional with sign-indefinite matrices. Its solution is obtained by the guar...
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2023-09-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | http://mathizv.isu.ru/en/article/file?id=1457 |
| _version_ | 1797685205320859648 |
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| author | V.A. Srochko V.G. Antonik |
| author_facet | V.A. Srochko V.G. Antonik |
| author_sort | V.A. Srochko |
| collection | DOAJ |
| description | Two linear-quadratic problems are considered on the set of piecewise-constant controls. The first problem contains a discrete perturbation on the right side of the controlled system and uncertain parameters in a quadratic functional with sign-indefinite matrices. Its solution is obtained by the guaranteed result rule and is implemented in the form of a finite-dimensional minimax problem. There are obtained conditions for the parameters that convert the objective function to a convex-concave structure and give the possibility of an effective solving of the problem. These are linear inequalities containing extreme eigenvalues of symmetric matrices. The second problem is related to the functional in the discrete variant, which is defined as the deviation of the phase trajectory from consecutive time realizations of the external influence. It gives the opportunity of the step by step searching of the extremmum at each node point of the time interval. Local problems can be effectively solved in a finite number of iterations. |
| first_indexed | 2024-03-12T00:41:44Z |
| format | Article |
| id | doaj.art-efe5bee99df64b88970f59d42c9768fd |
| institution | Directory Open Access Journal |
| issn | 1997-7670 2541-8785 |
| language | English |
| last_indexed | 2024-03-12T00:41:44Z |
| publishDate | 2023-09-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj.art-efe5bee99df64b88970f59d42c9768fd2023-09-15T07:32:19ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852023-09-014512436https://doi.org/10.26516/1997-7670.2023.45.24Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External ActionsV.A. SrochkoV.G. AntonikTwo linear-quadratic problems are considered on the set of piecewise-constant controls. The first problem contains a discrete perturbation on the right side of the controlled system and uncertain parameters in a quadratic functional with sign-indefinite matrices. Its solution is obtained by the guaranteed result rule and is implemented in the form of a finite-dimensional minimax problem. There are obtained conditions for the parameters that convert the objective function to a convex-concave structure and give the possibility of an effective solving of the problem. These are linear inequalities containing extreme eigenvalues of symmetric matrices. The second problem is related to the functional in the discrete variant, which is defined as the deviation of the phase trajectory from consecutive time realizations of the external influence. It gives the opportunity of the step by step searching of the extremmum at each node point of the time interval. Local problems can be effectively solved in a finite number of iterations.http://mathizv.isu.ru/en/article/file?id=1457linear-quadratic problemsdiscrete actions to system and functionalreduction to convex problems |
| spellingShingle | V.A. Srochko V.G. Antonik Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions Известия Иркутского государственного университета: Серия "Математика" linear-quadratic problems discrete actions to system and functional reduction to convex problems |
| title | Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions |
| title_full | Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions |
| title_fullStr | Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions |
| title_full_unstemmed | Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions |
| title_short | Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions |
| title_sort | resolution of linear quadratic problems in a discrete continuous format with external actions |
| topic | linear-quadratic problems discrete actions to system and functional reduction to convex problems |
| url | http://mathizv.isu.ru/en/article/file?id=1457 |
| work_keys_str_mv | AT vasrochko resolutionoflinearquadraticproblemsinadiscretecontinuousformatwithexternalactions AT vgantonik resolutionoflinearquadraticproblemsinadiscretecontinuousformatwithexternalactions |