Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control Problem
This paper is devoted to the construction of a zero-order approximation of the solution of a three-time scale singular perturbed linear-quadratic optimal control problem with the help of the direct scheme method. The algorithm of the method consists in immediate substituting a postulated asymptotic...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2015-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/233 |
| _version_ | 1797877862062096384 |
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| author | M. A. Kalashnikova |
| author_facet | M. A. Kalashnikova |
| author_sort | M. A. Kalashnikova |
| collection | DOAJ |
| description | This paper is devoted to the construction of a zero-order approximation of the solution of a three-time scale singular perturbed linear-quadratic optimal control problem with the help of the direct scheme method. The algorithm of the method consists in immediate substituting a postulated asymptotic expansion of solution into the problem condition and constructing a family of control problems to define the terms of the asymptotic expansion. Asymptotic approximation of the solution contains regular functions and four boundary ones of exponential type which are determined from the five linearquadratic optimal control problems. It is shown, that the system of equations for a zero-order approximation appeared from control optimality conditions of the initial perturbed problem corresponds to control optimality conditions appeared in respective five optimal control problems constructed for finding zero-order asymptotic approximation with the help of the direct scheme method. An illustrative example is given. |
| first_indexed | 2024-04-10T02:24:39Z |
| format | Article |
| id | doaj.art-30527d2047e14b9d902dd0d655109870 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:24:39Z |
| publishDate | 2015-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-30527d2047e14b9d902dd0d6551098702023-03-13T08:07:33ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-02-012218510410.18255/1818-1015-2015-1-85-104226Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control ProblemM. A. Kalashnikova0Воронежский государственный университетThis paper is devoted to the construction of a zero-order approximation of the solution of a three-time scale singular perturbed linear-quadratic optimal control problem with the help of the direct scheme method. The algorithm of the method consists in immediate substituting a postulated asymptotic expansion of solution into the problem condition and constructing a family of control problems to define the terms of the asymptotic expansion. Asymptotic approximation of the solution contains regular functions and four boundary ones of exponential type which are determined from the five linearquadratic optimal control problems. It is shown, that the system of equations for a zero-order approximation appeared from control optimality conditions of the initial perturbed problem corresponds to control optimality conditions appeared in respective five optimal control problems constructed for finding zero-order asymptotic approximation with the help of the direct scheme method. An illustrative example is given.https://www.mais-journal.ru/jour/article/view/233линейно-квадратичная задача оптимального управлениясингулярные возмущенияасимптотическое разложениеразнотемповые системы |
| spellingShingle | M. A. Kalashnikova Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control Problem Моделирование и анализ информационных систем линейно-квадратичная задача оптимального управления сингулярные возмущения асимптотическое разложение разнотемповые системы |
| title | Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control Problem |
| title_full | Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control Problem |
| title_fullStr | Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control Problem |
| title_full_unstemmed | Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control Problem |
| title_short | Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control Problem |
| title_sort | zero order approximation of three time scale singular linear quadratic optimal control problem |
| topic | линейно-квадратичная задача оптимального управления сингулярные возмущения асимптотическое разложение разнотемповые системы |
| url | https://www.mais-journal.ru/jour/article/view/233 |
| work_keys_str_mv | AT makalashnikova zeroorderapproximationofthreetimescalesingularlinearquadraticoptimalcontrolproblem |