L'équation de Hamilton-Jacobi en contrôle optimal
The main object of this thesis is the application of new methods from nonsmooth analysis and which use the Hamilton-Jacobi equation for the study of certain problems in control theory. There are three parts in our work: * In the first part we develop a new duality result in control theory. This resu...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | masterThesis |
| منشور في: |
2003
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/7407 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php https://tel.archives-ouvertes.fr/tel-00003973/ |
| الوسوم: |
إضافة وسم
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| _version_ | 1864513482108436480 |
|---|---|
| author | Nour, Chadi |
| author_facet | Nour, Chadi |
| author_role | author |
| dc.creator.none.fl_str_mv | Nour, Chadi |
| dc.date.none.fl_str_mv | 2003 2003-12-10 2018-04-18T08:57:24Z 2018-04-18T08:57:24Z |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10725/7407 Nour, C. (2003). L'équation de Hamlilton-Jacobi en contrôle optimal: dualité et géodésiques (Doctoral dissertation, Université Claude Bernard-Lyon I). http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php https://tel.archives-ouvertes.fr/tel-00003973/ |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | L' Universite Clause Bernard- Lyon 1 |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Hamilton-Jacobi equations Control theory |
| dc.title.none.fl_str_mv | L'équation de Hamilton-Jacobi en contrôle optimal dualité et géodésiques |
| dc.type.none.fl_str_mv | Thesis info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/masterThesis |
| description | The main object of this thesis is the application of new methods from nonsmooth analysis and which use the Hamilton-Jacobi equation for the study of certain problems in control theory. There are three parts in our work: * In the first part we develop a new duality result in control theory. This result generalizes, in a number of ways, the Vinter's duality (1993) and gives a new characterization of the minimal time function. * The second part is devoted to the study of the Hamilton-Jacobi equation of minimal time, but in a domain which contains the origin. We prove the existence of (minimal) solutions of this equation and we show that these solutions are closely linked to global geodesics trajectories. * In the third part, we study the existence of minimal loop trajectories for a control system. We give a necessary and sufficient conditions for the existence of this type of trajectories at a given point. |
| eu_rights_str_mv | openAccess |
| format | masterThesis |
| id | LAURepo_5b323f4ffd95e6b04ab9f9cd913e852b |
| identifier_str_mv | Nour, C. (2003). L'équation de Hamlilton-Jacobi en contrôle optimal: dualité et géodésiques (Doctoral dissertation, Université Claude Bernard-Lyon I). |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/7407 |
| publishDate | 2003 |
| publisher.none.fl_str_mv | L' Universite Clause Bernard- Lyon 1 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | L'équation de Hamilton-Jacobi en contrôle optimaldualité et géodésiquesNour, ChadiHamilton-Jacobi equationsControl theoryThe main object of this thesis is the application of new methods from nonsmooth analysis and which use the Hamilton-Jacobi equation for the study of certain problems in control theory. There are three parts in our work: * In the first part we develop a new duality result in control theory. This result generalizes, in a number of ways, the Vinter's duality (1993) and gives a new characterization of the minimal time function. * The second part is devoted to the study of the Hamilton-Jacobi equation of minimal time, but in a domain which contains the origin. We prove the existence of (minimal) solutions of this equation and we show that these solutions are closely linked to global geodesics trajectories. * In the third part, we study the existence of minimal loop trajectories for a control system. We give a necessary and sufficient conditions for the existence of this type of trajectories at a given point.N/Axii, 133 p. : illIncludes bibliographical referencesL' Universite Clause Bernard- Lyon 12018-04-18T08:57:24Z2018-04-18T08:57:24Z20032003-12-10Thesisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://hdl.handle.net/10725/7407Nour, C. (2003). L'équation de Hamlilton-Jacobi en contrôle optimal: dualité et géodésiques (Doctoral dissertation, Université Claude Bernard-Lyon I).http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.phphttps://tel.archives-ouvertes.fr/tel-00003973/eninfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/74072021-11-10T11:27:08Z |
| spellingShingle | L'équation de Hamilton-Jacobi en contrôle optimal Nour, Chadi Hamilton-Jacobi equations Control theory |
| status_str | publishedVersion |
| title | L'équation de Hamilton-Jacobi en contrôle optimal |
| title_full | L'équation de Hamilton-Jacobi en contrôle optimal |
| title_fullStr | L'équation de Hamilton-Jacobi en contrôle optimal |
| title_full_unstemmed | L'équation de Hamilton-Jacobi en contrôle optimal |
| title_short | L'équation de Hamilton-Jacobi en contrôle optimal |
| title_sort | L'équation de Hamilton-Jacobi en contrôle optimal |
| topic | Hamilton-Jacobi equations Control theory |
| url | http://hdl.handle.net/10725/7407 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php https://tel.archives-ouvertes.fr/tel-00003973/ |