On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients
The paper deals with a formalism of constructing a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic optimal control problem with discontinuous coefficients. This formalism is based on immediate substituting a postulated asymptotic expansion of boundary l...
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| Format: | Article |
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| Language: | English |
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Yaroslavl State University
2010-03-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/1024 |
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| collection | DOAJ |
| description | The paper deals with a formalism of constructing a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic optimal control problem with discontinuous coefficients. This formalism is based on immediate substituting a postulated asymptotic expansion of boundary layer type for the solution into the problem condition and on defining four optimal control problems for finding asymptotics terms. The unique solvability of the problems, the solutions of which form the zero order approximation for the asymptotic solution, is proven. An illustrative example is given. |
| format | Article |
| id | doaj-art-58f7076db763472ebd286dfed7b6f0cd |
| institution | DOAJ |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2010-03-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-58f7076db763472ebd286dfed7b6f0cd2025-08-20T03:22:04ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172010-03-0117193116765On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients01Воронежская государственная лесотехническая академияВоронежская государственная лесотехническая академияThe paper deals with a formalism of constructing a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic optimal control problem with discontinuous coefficients. This formalism is based on immediate substituting a postulated asymptotic expansion of boundary layer type for the solution into the problem condition and on defining four optimal control problems for finding asymptotics terms. The unique solvability of the problems, the solutions of which form the zero order approximation for the asymptotic solution, is proven. An illustrative example is given.https://www.mais-journal.ru/jour/article/view/1024linear-quadratic optimal control problemsingular perturbationsdiscontinuous coefficientsasymptotic expansion |
| spellingShingle | On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients Моделирование и анализ информационных систем linear-quadratic optimal control problem singular perturbations discontinuous coefficients asymptotic expansion |
| title | On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients |
| title_full | On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients |
| title_fullStr | On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients |
| title_full_unstemmed | On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients |
| title_short | On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients |
| title_sort | on a zero order approximation of an asymptotic solution for a singularly perturbed linear quadratic control problem with discontinuous coefficients |
| topic | linear-quadratic optimal control problem singular perturbations discontinuous coefficients asymptotic expansion |
| url | https://www.mais-journal.ru/jour/article/view/1024 |