Solution Continuation on a Discontinuity Set
The movement of an object characterized by ordinary differential equations (ODE) with discontinuous right-hand sides along the surface of a gap is called a sliding mode. It is required to find the connection of the right-slip characteristics of the system (the system to continue the solution on the su...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2016-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/303 |
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| author | A. M. Tsirlin |
| author_facet | A. M. Tsirlin |
| author_sort | A. M. Tsirlin |
| collection | DOAJ |
| description | The movement of an object characterized by ordinary differential equations (ODE) with discontinuous right-hand sides along the surface of a gap is called a sliding mode. It is required to find the connection of the right-slip characteristics of the system (the system to continue the solution on the surface of the gap). The article prompted a sequel based on the solution of the averaged optimization. It is shown that for the known examples of methods for solving optimization averaged lead to results coinciding with the method of A.F. Filippov and allow to extend these techniques to a wide class of multidimensional problems. Optimality conditions set forth averaged nonlinear programming and examples of their use in the case of ordinary and degenerate solutions. |
| format | Article |
| id | doaj-art-ededc414e32c4fdd91ed5d0ab21bc08f |
| institution | DOAJ |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2016-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-ededc414e32c4fdd91ed5d0ab21bc08f2025-08-20T03:22:04ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172016-02-01231122210.18255/1818-1015-2016-1-12-22279Solution Continuation on a Discontinuity SetA. M. Tsirlin0Program Systems Institute of RAS Petra 1 str., 4a, Veskovo Jaroslavskoy, 152020, RussiaThe movement of an object characterized by ordinary differential equations (ODE) with discontinuous right-hand sides along the surface of a gap is called a sliding mode. It is required to find the connection of the right-slip characteristics of the system (the system to continue the solution on the surface of the gap). The article prompted a sequel based on the solution of the averaged optimization. It is shown that for the known examples of methods for solving optimization averaged lead to results coinciding with the method of A.F. Filippov and allow to extend these techniques to a wide class of multidimensional problems. Optimality conditions set forth averaged nonlinear programming and examples of their use in the case of ordinary and degenerate solutions.https://www.mais-journal.ru/jour/article/view/303differential equations with discontinuous velocitysliding modesaveraged optimization |
| spellingShingle | A. M. Tsirlin Solution Continuation on a Discontinuity Set Моделирование и анализ информационных систем differential equations with discontinuous velocity sliding modes averaged optimization |
| title | Solution Continuation on a Discontinuity Set |
| title_full | Solution Continuation on a Discontinuity Set |
| title_fullStr | Solution Continuation on a Discontinuity Set |
| title_full_unstemmed | Solution Continuation on a Discontinuity Set |
| title_short | Solution Continuation on a Discontinuity Set |
| title_sort | solution continuation on a discontinuity set |
| topic | differential equations with discontinuous velocity sliding modes averaged optimization |
| url | https://www.mais-journal.ru/jour/article/view/303 |
| work_keys_str_mv | AT amtsirlin solutioncontinuationonadiscontinuityset |