Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum Approaches
The optimal control is the process of finding a control strategy that extreme some performance index for a dynamic system (partial differential equation) over the class of admissibility. The present work deals with a problem of fixed boundary with a control manipulated in the structure of the partia...
| Main Authors: | , |
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| Format: | Article |
| Language: | Arabic |
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Al-Mustansiriyah University
2023-09-01
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| Series: | Mustansiriyah Journal of Science |
| Subjects: | |
| Online Access: | https://mjs.uomustansiriyah.edu.iq/index.php/MJS/article/view/1104 |
| _version_ | 1797670083235938304 |
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| author | Amal S. Hameed Radhi A. Zaboon |
| author_facet | Amal S. Hameed Radhi A. Zaboon |
| author_sort | Amal S. Hameed |
| collection | DOAJ |
| description | The optimal control is the process of finding a control strategy that extreme some performance index for a dynamic system (partial differential equation) over the class of admissibility. The present work deals with a problem of fixed boundary with a control manipulated in the structure of the partial differential equation. An attractive computational method for determining the optimal control of unconstrained linear dynamic system with a quadratic performance index is presented. In the proposed method the difference between every state variable and its initial condition is represented by a finite - term polynomial series, this representation leads to a system of linear algebraic equations which represents the necessary condition of optimality. The linear algebraic system is solved by using two approaches namely the variational iteration method and the minimization approach for unconstrained optimization problem with estimation of gradient and Hessian matrix. These approaches are illustrated by two application examples. |
| first_indexed | 2024-03-11T20:54:34Z |
| format | Article |
| id | doaj.art-23963ac2f6094ac9891aecddfab7e27d |
| institution | Directory Open Access Journal |
| issn | 1814-635X 2521-3520 |
| language | Arabic |
| last_indexed | 2024-03-11T20:54:34Z |
| publishDate | 2023-09-01 |
| publisher | Al-Mustansiriyah University |
| record_format | Article |
| series | Mustansiriyah Journal of Science |
| spelling | doaj.art-23963ac2f6094ac9891aecddfab7e27d2023-09-30T15:47:45ZaraAl-Mustansiriyah UniversityMustansiriyah Journal of Science1814-635X2521-35202023-09-0134310.23851/mjs.v34i3.1104Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum ApproachesAmal S. Hameed0Radhi A. Zaboon1Department of Mathematics, College of Science, University of Diyala, 32001 Diyala, IRAQ.Department of Mathematics, College of Science, Mustansiriyah University, 10052 Baghdad, IRAQ.The optimal control is the process of finding a control strategy that extreme some performance index for a dynamic system (partial differential equation) over the class of admissibility. The present work deals with a problem of fixed boundary with a control manipulated in the structure of the partial differential equation. An attractive computational method for determining the optimal control of unconstrained linear dynamic system with a quadratic performance index is presented. In the proposed method the difference between every state variable and its initial condition is represented by a finite - term polynomial series, this representation leads to a system of linear algebraic equations which represents the necessary condition of optimality. The linear algebraic system is solved by using two approaches namely the variational iteration method and the minimization approach for unconstrained optimization problem with estimation of gradient and Hessian matrix. These approaches are illustrated by two application examples.https://mjs.uomustansiriyah.edu.iq/index.php/MJS/article/view/1104Optimal control problemslinear distributed parameter systemsvariational methodapproximate solutionspolynomial based approximation |
| spellingShingle | Amal S. Hameed Radhi A. Zaboon Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum Approaches Mustansiriyah Journal of Science Optimal control problems linear distributed parameter systems variational method approximate solutions polynomial based approximation |
| title | Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum Approaches |
| title_full | Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum Approaches |
| title_fullStr | Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum Approaches |
| title_full_unstemmed | Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum Approaches |
| title_short | Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum Approaches |
| title_sort | approximate solutions for optimal control of fixed boundary value problems using variational and minimum approaches |
| topic | Optimal control problems linear distributed parameter systems variational method approximate solutions polynomial based approximation |
| url | https://mjs.uomustansiriyah.edu.iq/index.php/MJS/article/view/1104 |
| work_keys_str_mv | AT amalshameed approximatesolutionsforoptimalcontroloffixedboundaryvalueproblemsusingvariationalandminimumapproaches AT radhiazaboon approximatesolutionsforoptimalcontroloffixedboundaryvalueproblemsusingvariationalandminimumapproaches |