Subdifferential properties of the minimal time function of linear control systems
We present several formulae for the proximal and Fréchet subdifferentials of the minimal time function defined by a linear control system and a target set. At every point inside the target set, the proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of the target...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Springer
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/40464 |
| _version_ | 1848755878495256576 |
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| author | Jiang, Y. He, Y. Sun, Jie |
| author_facet | Jiang, Y. He, Y. Sun, Jie |
| author_sort | Jiang, Y. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We present several formulae for the proximal and Fréchet subdifferentials of the minimal time function defined by a linear control system and a target set. At every point inside the target set, the proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of the target set and an upper level set of a so-called Hamiltonian function which depends only on the linear control system. At every point outside the target set, under a mild assumption, proximal/Fréchet subdifferential is the intersection of the proximal/ Fréchet normal cone of an enlargement of the target set and a level set of the Hamiltonian function. |
| first_indexed | 2025-11-14T09:03:18Z |
| format | Journal Article |
| id | curtin-20.500.11937-40464 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:03:18Z |
| publishDate | 2011 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-404642017-09-13T13:38:56Z Subdifferential properties of the minimal time function of linear control systems Jiang, Y. He, Y. Sun, Jie We present several formulae for the proximal and Fréchet subdifferentials of the minimal time function defined by a linear control system and a target set. At every point inside the target set, the proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of the target set and an upper level set of a so-called Hamiltonian function which depends only on the linear control system. At every point outside the target set, under a mild assumption, proximal/Fréchet subdifferential is the intersection of the proximal/ Fréchet normal cone of an enlargement of the target set and a level set of the Hamiltonian function. 2011 Journal Article http://hdl.handle.net/20.500.11937/40464 10.1007/s10898-010-9633-6 Springer restricted |
| spellingShingle | Jiang, Y. He, Y. Sun, Jie Subdifferential properties of the minimal time function of linear control systems |
| title | Subdifferential properties of the minimal time function of linear control systems |
| title_full | Subdifferential properties of the minimal time function of linear control systems |
| title_fullStr | Subdifferential properties of the minimal time function of linear control systems |
| title_full_unstemmed | Subdifferential properties of the minimal time function of linear control systems |
| title_short | Subdifferential properties of the minimal time function of linear control systems |
| title_sort | subdifferential properties of the minimal time function of linear control systems |
| url | http://hdl.handle.net/20.500.11937/40464 |