An optimal control problem involving impulsive integrodifferential systems
In this article, we consider a class of optimal control problems involving dynamical systems described by impulsive integrodifferential equations. First, we approximate the integral kernel of the integral equation by a finite expansion of the shifted Chebyshev polynomial. Through this process, the o...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Taylor and Francis
2007
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| Online Access: | http://hdl.handle.net/20.500.11937/34875 |
| _version_ | 1848754342131138560 |
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| author | Wu, C. Teo, Kok Lay Zhao, Y. Yan, W. |
| author_facet | Wu, C. Teo, Kok Lay Zhao, Y. Yan, W. |
| author_sort | Wu, C. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this article, we consider a class of optimal control problems involving dynamical systems described by impulsive integrodifferential equations. First, we approximate the integral kernel of the integral equation by a finite expansion of the shifted Chebyshev polynomial. Through this process, the optimal control problem is approximated by a sequence of optimal control problems involving only impulsive ordinary differential equations. Each of them can be viewed as a nonlinear optimization problem. For each of these approximated problems, the gradient formula of the cost functional can be derived and hence can be solved by many efficient optimization techniques. Consequently, the optimal control software, MISER, is applicable for the purpose. Then, we present some convergence results showing the relationship between the sequence of the optimal controls of the approximated problems and that of the original problem. Finally, a numerical example is presented to illustrate the efficiency of the proposed method. |
| first_indexed | 2025-11-14T08:38:53Z |
| format | Journal Article |
| id | curtin-20.500.11937-34875 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:38:53Z |
| publishDate | 2007 |
| publisher | Taylor and Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-348752017-09-13T16:08:11Z An optimal control problem involving impulsive integrodifferential systems Wu, C. Teo, Kok Lay Zhao, Y. Yan, W. In this article, we consider a class of optimal control problems involving dynamical systems described by impulsive integrodifferential equations. First, we approximate the integral kernel of the integral equation by a finite expansion of the shifted Chebyshev polynomial. Through this process, the optimal control problem is approximated by a sequence of optimal control problems involving only impulsive ordinary differential equations. Each of them can be viewed as a nonlinear optimization problem. For each of these approximated problems, the gradient formula of the cost functional can be derived and hence can be solved by many efficient optimization techniques. Consequently, the optimal control software, MISER, is applicable for the purpose. Then, we present some convergence results showing the relationship between the sequence of the optimal controls of the approximated problems and that of the original problem. Finally, a numerical example is presented to illustrate the efficiency of the proposed method. 2007 Journal Article http://hdl.handle.net/20.500.11937/34875 10.1080/10556780601135688 Taylor and Francis restricted |
| spellingShingle | Wu, C. Teo, Kok Lay Zhao, Y. Yan, W. An optimal control problem involving impulsive integrodifferential systems |
| title | An optimal control problem involving impulsive integrodifferential systems |
| title_full | An optimal control problem involving impulsive integrodifferential systems |
| title_fullStr | An optimal control problem involving impulsive integrodifferential systems |
| title_full_unstemmed | An optimal control problem involving impulsive integrodifferential systems |
| title_short | An optimal control problem involving impulsive integrodifferential systems |
| title_sort | optimal control problem involving impulsive integrodifferential systems |
| url | http://hdl.handle.net/20.500.11937/34875 |