Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019)
The main objective of this thesis is to study the '0-convexity of the epigraph of the bilateral minimal time function for a nonlinear control system. There are three parts in our work. In the first part, we study the variational analysis of the bilateral minimal time function under the Standing...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | masterThesis |
| منشور في: |
2019
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/11583 https://doi.org/10.26756/th.2019.149 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
| الوسوم: |
إضافة وسم
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| _version_ | 1864513489243996160 |
|---|---|
| author | Chamoun, Samara Sarkis |
| author_facet | Chamoun, Samara Sarkis |
| author_role | author |
| dc.creator.none.fl_str_mv | Chamoun, Samara Sarkis |
| dc.date.none.fl_str_mv | 2019-11-27T08:18:09Z 2019-11-27T08:18:09Z 2019 2019-11-27 2019-05-02 |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10725/11583 https://doi.org/10.26756/th.2019.149 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | Lebanese American University |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Lebanese American University -- Dissertations Dissertations, Academic Nonlinear control theory Mathematical optimization Calculus of variations |
| dc.title.none.fl_str_mv | Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019) |
| dc.type.none.fl_str_mv | Thesis info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/masterThesis |
| description | The main objective of this thesis is to study the '0-convexity of the epigraph of the bilateral minimal time function for a nonlinear control system. There are three parts in our work. In the first part, we study the variational analysis of the bilateral minimal time function under the Standing Hypotheses. One of the main results of this part is a relation between the proximal normal cones to sub-level sets of the bilateral minimal time function and its epigraph. The second part is devoted to the generation of sensitivity relations for the bilateral minimal time function. More precisely, we prove some propagation results for the proximal (horizontal) subdifferential along optimal trajectories. In the third part, we use the results of the first two parts to study the regularity of the bilateral minimal time function for a nonlinear control system. Among other assumptions, we prove that the continuity of the bilateral minimal time function near a point is suffcient for the '0-convexity of its epigraph near this point. This extends, to the nonlinear case, a similar result proved by Nour in 2013 for a linear control system. |
| eu_rights_str_mv | openAccess |
| format | masterThesis |
| id | LAURepo_04b34e7eab1fecea3fe3fed4b13a921f |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/11583 |
| publishDate | 2019 |
| publisher.none.fl_str_mv | Lebanese American University |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019)Chamoun, Samara SarkisLebanese American University -- DissertationsDissertations, AcademicNonlinear control theoryMathematical optimizationCalculus of variationsThe main objective of this thesis is to study the '0-convexity of the epigraph of the bilateral minimal time function for a nonlinear control system. There are three parts in our work. In the first part, we study the variational analysis of the bilateral minimal time function under the Standing Hypotheses. One of the main results of this part is a relation between the proximal normal cones to sub-level sets of the bilateral minimal time function and its epigraph. The second part is devoted to the generation of sensitivity relations for the bilateral minimal time function. More precisely, we prove some propagation results for the proximal (horizontal) subdifferential along optimal trajectories. In the third part, we use the results of the first two parts to study the regularity of the bilateral minimal time function for a nonlinear control system. Among other assumptions, we prove that the continuity of the bilateral minimal time function near a point is suffcient for the '0-convexity of its epigraph near this point. This extends, to the nonlinear case, a similar result proved by Nour in 2013 for a linear control system.N/A1 hard copy: xi, 55 leaves: ill.; 30 cm. available at RNL.Bibliograpgy: (leaves 52-55).Lebanese American University2019-11-27T08:18:09Z2019-11-27T08:18:09Z20192019-11-272019-05-02Thesisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://hdl.handle.net/10725/11583https://doi.org/10.26756/th.2019.149http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.phpeninfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/115832021-03-19T10:47:39Z |
| spellingShingle | Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019) Chamoun, Samara Sarkis Lebanese American University -- Dissertations Dissertations, Academic Nonlinear control theory Mathematical optimization Calculus of variations |
| status_str | publishedVersion |
| title | Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019) |
| title_full | Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019) |
| title_fullStr | Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019) |
| title_full_unstemmed | Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019) |
| title_short | Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019) |
| title_sort | Variational analysis and sensitivity relations of the bilateral minimal time functions for nonlinear differential inclusions. (c2019) |
| topic | Lebanese American University -- Dissertations Dissertations, Academic Nonlinear control theory Mathematical optimization Calculus of variations |
| url | http://hdl.handle.net/10725/11583 https://doi.org/10.26756/th.2019.149 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |