Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems
The minimal time function of a class of semilinear control systems is considered in Banach spaces, with the target set being a closed ball. It is shown that the minimal time functions of the Yosida approximation equations converge to the minimal time function of the semilinear control system. Comple...
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Published: |
2015
|
| Online Access: | http://hdl.handle.net/20.500.11937/15548 |
| _version_ | 1848748923015921664 |
|---|---|
| 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 | The minimal time function of a class of semilinear control systems is considered in Banach spaces, with the target set being a closed ball. It is shown that the minimal time functions of the Yosida approximation equations converge to the minimal time function of the semilinear control system. Complete characterization is established for the subdifferential of the minimal time function satisfying the Hamilton–Jacobi–Bellman equation. These results extend the theory of finite dimensional linear control systems to infinite dimensional semilinear control systems. |
| first_indexed | 2025-11-14T07:12:45Z |
| format | Journal Article |
| id | curtin-20.500.11937-15548 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:12:45Z |
| publishDate | 2015 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-155482019-02-19T05:34:54Z Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems Jiang, Y. He, Y. Sun, Jie The minimal time function of a class of semilinear control systems is considered in Banach spaces, with the target set being a closed ball. It is shown that the minimal time functions of the Yosida approximation equations converge to the minimal time function of the semilinear control system. Complete characterization is established for the subdifferential of the minimal time function satisfying the Hamilton–Jacobi–Bellman equation. These results extend the theory of finite dimensional linear control systems to infinite dimensional semilinear control systems. 2015 Journal Article http://hdl.handle.net/20.500.11937/15548 10.1007/s10957-015-0848-z fulltext |
| spellingShingle | Jiang, Y. He, Y. Sun, Jie Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems |
| title | Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems |
| title_full | Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems |
| title_fullStr | Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems |
| title_full_unstemmed | Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems |
| title_short | Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems |
| title_sort | proximal analysis and the minimal time function of a class of semilinear control systems |
| url | http://hdl.handle.net/20.500.11937/15548 |