Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem
In this paper, we first present formulas for computing the Fréchet subdifferentials and Fréchet singular subdifferentials of the minimal time function <inline-formula> <tex-math notation="LaTeX">$\mathscr {T}$ </tex-math></inline-formula> for a...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9026975/ |
| _version_ | 1811209800871051264 |
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| author | Luong V. Nguyen Nguyen T. Thu |
| author_facet | Luong V. Nguyen Nguyen T. Thu |
| author_sort | Luong V. Nguyen |
| collection | DOAJ |
| description | In this paper, we first present formulas for computing the Fréchet subdifferentials and Fréchet singular subdifferentials of the minimal time function <inline-formula> <tex-math notation="LaTeX">$\mathscr {T}$ </tex-math></inline-formula> for a differential inclusion in <inline-formula> <tex-math notation="LaTeX">$\mathbb {R}^{n}$ </tex-math></inline-formula> with a general target <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>. These formulas are characterized in terms of Fréchet normal cones to a sub-level set of <inline-formula> <tex-math notation="LaTeX">$\mathscr {T}$ </tex-math></inline-formula> and a level set of the minimized Hamiltonian associated with the differential inclusion. Our results extend, improve and complement to existing results. An application to sensitivity analysis for a class of time optimal control problems is also given. |
| first_indexed | 2024-04-12T04:45:02Z |
| format | Article |
| id | doaj.art-bc9d03ea2ca442209e67f94480daafcc |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-12T04:45:02Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-bc9d03ea2ca442209e67f94480daafcc2022-12-22T03:47:31ZengIEEEIEEE Access2169-35362020-01-018465964660410.1109/ACCESS.2020.29790619026975Fréchet Analysis and Sensitivity Relations for the Optimal Time ProblemLuong V. Nguyen0https://orcid.org/0000-0002-5784-5552Nguyen T. Thu1Laboratory of Theoretical and Computational Biophysics, Ton Duc Thang University, Ho Chi Minh City, VietnamFaculty of Natural Sciences, Hong Duc University, Thanh Hoa, VietnamIn this paper, we first present formulas for computing the Fréchet subdifferentials and Fréchet singular subdifferentials of the minimal time function <inline-formula> <tex-math notation="LaTeX">$\mathscr {T}$ </tex-math></inline-formula> for a differential inclusion in <inline-formula> <tex-math notation="LaTeX">$\mathbb {R}^{n}$ </tex-math></inline-formula> with a general target <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>. These formulas are characterized in terms of Fréchet normal cones to a sub-level set of <inline-formula> <tex-math notation="LaTeX">$\mathscr {T}$ </tex-math></inline-formula> and a level set of the minimized Hamiltonian associated with the differential inclusion. Our results extend, improve and complement to existing results. An application to sensitivity analysis for a class of time optimal control problems is also given.https://ieeexplore.ieee.org/document/9026975/Differential inclusionsFréchet subdifferentialsminimum time functionsensitivity relations |
| spellingShingle | Luong V. Nguyen Nguyen T. Thu Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem IEEE Access Differential inclusions Fréchet subdifferentials minimum time function sensitivity relations |
| title | Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem |
| title_full | Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem |
| title_fullStr | Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem |
| title_full_unstemmed | Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem |
| title_short | Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem |
| title_sort | fr x00e9 chet analysis and sensitivity relations for the optimal time problem |
| topic | Differential inclusions Fréchet subdifferentials minimum time function sensitivity relations |
| url | https://ieeexplore.ieee.org/document/9026975/ |
| work_keys_str_mv | AT luongvnguyen frx00e9chetanalysisandsensitivityrelationsfortheoptimaltimeproblem AT nguyentthu frx00e9chetanalysisandsensitivityrelationsfortheoptimaltimeproblem |