Singularly perturbed control problems in the case of the stability of the spectrum of the matrix of an optimal system
The paper considers a singularly perturbed control problem with a quadratic quality functional. Such problems in their standard formulation under known spectrum restrictions (the points of the spectrum of the optimal system are not purely imaginary and are located symmetrically with respect to the...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2019-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/287 |
| _version_ | 1797372679625375744 |
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| author | A.A. Bobodzhanov B.T. Kalimbetov V.F. Safonov |
| author_facet | A.A. Bobodzhanov B.T. Kalimbetov V.F. Safonov |
| author_sort | A.A. Bobodzhanov |
| collection | DOAJ |
| description |
The paper considers a singularly perturbed control problem with a quadratic quality functional. Such problems in their standard formulation under known spectrum restrictions (the points of the spectrum of the optimal system are not purely imaginary and are located symmetrically with respect to the imaginary axis) were previously considered using the Vasilyeva - Butuzov method of boundary functions. If at least one of the points of the spectrum for some values of the independent variable falls on the imaginary axis, the boundary functions method does not work. It is precisely this situation with the assumption of purely imaginary points of the spectrum that is investigated in this paper. In this case, you have to develop a different approach based on the ideas of the regularization method S.A. Lomov. It should also be noted that in the control problems considered earlier, the cost functional either did not depend on a small parameter at all, or allowed a smooth dependence on the parameter...
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| first_indexed | 2024-03-08T18:39:17Z |
| format | Article |
| id | doaj.art-c42896fcac6044f5808e66d4e48a146e |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:17Z |
| publishDate | 2019-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-c42896fcac6044f5808e66d4e48a146e2023-12-29T10:20:39ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112019-12-0196410.31489/2019m4/22-38Singularly perturbed control problems in the case of the stability of the spectrum of the matrix of an optimal systemA.A. BobodzhanovB.T. KalimbetovV.F. Safonov The paper considers a singularly perturbed control problem with a quadratic quality functional. Such problems in their standard formulation under known spectrum restrictions (the points of the spectrum of the optimal system are not purely imaginary and are located symmetrically with respect to the imaginary axis) were previously considered using the Vasilyeva - Butuzov method of boundary functions. If at least one of the points of the spectrum for some values of the independent variable falls on the imaginary axis, the boundary functions method does not work. It is precisely this situation with the assumption of purely imaginary points of the spectrum that is investigated in this paper. In this case, you have to develop a different approach based on the ideas of the regularization method S.A. Lomov. It should also be noted that in the control problems considered earlier, the cost functional either did not depend on a small parameter at all, or allowed a smooth dependence on the parameter... http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/287singularly perturbedPontryagin’s maximum principleregularizationasymptotic convergence |
| spellingShingle | A.A. Bobodzhanov B.T. Kalimbetov V.F. Safonov Singularly perturbed control problems in the case of the stability of the spectrum of the matrix of an optimal system Қарағанды университетінің хабаршысы. Математика сериясы singularly perturbed Pontryagin’s maximum principle regularization asymptotic convergence |
| title | Singularly perturbed control problems in the case of the stability of the spectrum of the matrix of an optimal system |
| title_full | Singularly perturbed control problems in the case of the stability of the spectrum of the matrix of an optimal system |
| title_fullStr | Singularly perturbed control problems in the case of the stability of the spectrum of the matrix of an optimal system |
| title_full_unstemmed | Singularly perturbed control problems in the case of the stability of the spectrum of the matrix of an optimal system |
| title_short | Singularly perturbed control problems in the case of the stability of the spectrum of the matrix of an optimal system |
| title_sort | singularly perturbed control problems in the case of the stability of the spectrum of the matrix of an optimal system |
| topic | singularly perturbed Pontryagin’s maximum principle regularization asymptotic convergence |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/287 |
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