On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation
<p>In this article, it is considered some questions of approximation solving of an optimal control problem for nonlinear partial pseudohyperbolic differential equations of the fifth order with initial-boundary value conditions and general view of the optimality criterion. Using the method of s...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2013-01-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | http://mais-journal.ru/jour/article/view/175 |
| _version_ | 1797969180035645440 |
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| author | T. K. Yuldashev |
| author_facet | T. K. Yuldashev |
| author_sort | T. K. Yuldashev |
| collection | DOAJ |
| description | <p>In this article, it is considered some questions of approximation solving of an optimal control problem for nonlinear partial pseudohyperbolic differential equations of the fifth order with initial-boundary value conditions and general view of the optimality criterion. Using the method of separation of variables in the form of a Fourier series reduces the generalized solution of the initial-boundary value problem to a countable system of nonlinear integral equations. By the aid of the methods of successive approximations and integral inequalities it is studied the one-value solvability of a finite system of nonlinear integral equations for the fixed values of the control, which are bounded by the given positive constant. It is estimated the permissible error with respect to a state of a ”shorter” generalized solution of the initial-boundary value problem. Further, it is proved that the control sequence is a minimizing sequence for the considered problem.</p> |
| first_indexed | 2024-04-11T02:58:07Z |
| format | Article |
| id | doaj.art-2212b723f00543b99dd27ade126893bd |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-11T02:58:07Z |
| publishDate | 2013-01-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-2212b723f00543b99dd27ade126893bd2023-01-02T14:28:19ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-01-012057889169On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic EquationT. K. Yuldashev0Сибирский государственный аэрокосмический университет им. академика М. Ф. Решетнева<p>In this article, it is considered some questions of approximation solving of an optimal control problem for nonlinear partial pseudohyperbolic differential equations of the fifth order with initial-boundary value conditions and general view of the optimality criterion. Using the method of separation of variables in the form of a Fourier series reduces the generalized solution of the initial-boundary value problem to a countable system of nonlinear integral equations. By the aid of the methods of successive approximations and integral inequalities it is studied the one-value solvability of a finite system of nonlinear integral equations for the fixed values of the control, which are bounded by the given positive constant. It is estimated the permissible error with respect to a state of a ”shorter” generalized solution of the initial-boundary value problem. Further, it is proved that the control sequence is a minimizing sequence for the considered problem.</p>http://mais-journal.ru/jour/article/view/175оптимальное управлениеобобщенная разрешимостьинтегральное тождествоприближенное решениеминимизация функционала |
| spellingShingle | T. K. Yuldashev On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation Моделирование и анализ информационных систем оптимальное управление обобщенная разрешимость интегральное тождество приближенное решение минимизация функционала |
| title | On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation |
| title_full | On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation |
| title_fullStr | On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation |
| title_full_unstemmed | On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation |
| title_short | On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation |
| title_sort | on a problem of optimal control for a nonlinear pseudohyperbolic equation |
| topic | оптимальное управление обобщенная разрешимость интегральное тождество приближенное решение минимизация функционала |
| url | http://mais-journal.ru/jour/article/view/175 |
| work_keys_str_mv | AT tkyuldashev onaproblemofoptimalcontrolforanonlinearpseudohyperbolicequation |