Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone
Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach....
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/585967 |
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| _version_ | 1832566474949001216 |
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| author | Yuan Wang Xiaochuan Luo Sai Li |
| author_facet | Yuan Wang Xiaochuan Luo Sai Li |
| author_sort | Yuan Wang |
| collection | DOAJ |
| description | Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations. |
| format | Article |
| id | doaj-art-504879f3696448b5aacd09ac96c6c187 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-504879f3696448b5aacd09ac96c6c1872025-02-03T01:04:04ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/585967585967Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling ZoneYuan Wang0Xiaochuan Luo1Sai Li2State Key Laboratory of Synthetical Automation for Process industries, Northeastern University, Shenyang 110004, ChinaState Key Laboratory of Synthetical Automation for Process industries, Northeastern University, Shenyang 110004, ChinaState Key Laboratory of Synthetical Automation for Process industries, Northeastern University, Shenyang 110004, ChinaOur work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.http://dx.doi.org/10.1155/2015/585967 |
| spellingShingle | Yuan Wang Xiaochuan Luo Sai Li Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone Advances in Mathematical Physics |
| title | Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone |
| title_full | Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone |
| title_fullStr | Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone |
| title_full_unstemmed | Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone |
| title_short | Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone |
| title_sort | optimal control method of parabolic partial differential equations and its application to heat transfer model in continuous cast secondary cooling zone |
| url | http://dx.doi.org/10.1155/2015/585967 |
| work_keys_str_mv | AT yuanwang optimalcontrolmethodofparabolicpartialdifferentialequationsanditsapplicationtoheattransfermodelincontinuouscastsecondarycoolingzone AT xiaochuanluo optimalcontrolmethodofparabolicpartialdifferentialequationsanditsapplicationtoheattransfermodelincontinuouscastsecondarycoolingzone AT saili optimalcontrolmethodofparabolicpartialdifferentialequationsanditsapplicationtoheattransfermodelincontinuouscastsecondarycoolingzone |