Hamilton-Jacobi-Bellman equations on time scales
In this paper, we consider a class of optimal control problems on time scales without state constraints, target conditions or the fixed terminal time. We first present and show a time scale version of the Bellman optimality principle. On this basis, using a chain rule of multivariables on time scale...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Pergamon
2009
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| Online Access: | http://hdl.handle.net/20.500.11937/3004 |
| _version_ | 1848744110373994496 |
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| author | Zhan, Z. Wei, W. Xu, Honglei |
| author_facet | Zhan, Z. Wei, W. Xu, Honglei |
| author_sort | Zhan, Z. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a class of optimal control problems on time scales without state constraints, target conditions or the fixed terminal time. We first present and show a time scale version of the Bellman optimality principle. On this basis, using a chain rule of multivariables on time scales, we will derive Hamilton-Jacobi-Bellman equations on a time scale for these kind of optimal control problems. Finally, the quantum time scale is considered as an example to illustrate our results. © 2009 Elsevier Ltd. All rights reserved. |
| first_indexed | 2025-11-14T05:56:15Z |
| format | Journal Article |
| id | curtin-20.500.11937-3004 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T05:56:15Z |
| publishDate | 2009 |
| publisher | Pergamon |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-30042017-09-13T14:45:10Z Hamilton-Jacobi-Bellman equations on time scales Zhan, Z. Wei, W. Xu, Honglei In this paper, we consider a class of optimal control problems on time scales without state constraints, target conditions or the fixed terminal time. We first present and show a time scale version of the Bellman optimality principle. On this basis, using a chain rule of multivariables on time scales, we will derive Hamilton-Jacobi-Bellman equations on a time scale for these kind of optimal control problems. Finally, the quantum time scale is considered as an example to illustrate our results. © 2009 Elsevier Ltd. All rights reserved. 2009 Journal Article http://hdl.handle.net/20.500.11937/3004 10.1016/j.mcm.2008.12.008 Pergamon unknown |
| spellingShingle | Zhan, Z. Wei, W. Xu, Honglei Hamilton-Jacobi-Bellman equations on time scales |
| title | Hamilton-Jacobi-Bellman equations on time scales |
| title_full | Hamilton-Jacobi-Bellman equations on time scales |
| title_fullStr | Hamilton-Jacobi-Bellman equations on time scales |
| title_full_unstemmed | Hamilton-Jacobi-Bellman equations on time scales |
| title_short | Hamilton-Jacobi-Bellman equations on time scales |
| title_sort | hamilton-jacobi-bellman equations on time scales |
| url | http://hdl.handle.net/20.500.11937/3004 |