Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension
The present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. Pontryagin maximum prin...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/493130 |
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| author | Ismail Kucuk Kenan Yildirim |
| author_facet | Ismail Kucuk Kenan Yildirim |
| author_sort | Ismail Kucuk |
| collection | DOAJ |
| description | The present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. Pontryagin maximum principle is derived to be a necessary condition for the controls of such systems to be optimal. With the aid of some convexity assumptions on the constraint functions, it is obtained that the maximum principle is also a sufficient condition for the optimality. |
| format | Article |
| id | doaj-art-5e1d4182345144b28e01a3a5ce6f3cc1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5e1d4182345144b28e01a3a5ce6f3cc12025-02-03T06:00:06ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/493130493130Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space DimensionIsmail Kucuk0Kenan Yildirim1Department of Mathematical Engineering, Yildiz Technical University, Istanbul, TurkeyDepartment of Mathematical Engineering, Yildiz Technical University, Istanbul, TurkeyThe present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. Pontryagin maximum principle is derived to be a necessary condition for the controls of such systems to be optimal. With the aid of some convexity assumptions on the constraint functions, it is obtained that the maximum principle is also a sufficient condition for the optimality.http://dx.doi.org/10.1155/2014/493130 |
| spellingShingle | Ismail Kucuk Kenan Yildirim Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension Abstract and Applied Analysis |
| title | Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension |
| title_full | Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension |
| title_fullStr | Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension |
| title_full_unstemmed | Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension |
| title_short | Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension |
| title_sort | necessary and sufficient conditions of optimality for a damped hyperbolic equation in one space dimension |
| url | http://dx.doi.org/10.1155/2014/493130 |
| work_keys_str_mv | AT ismailkucuk necessaryandsufficientconditionsofoptimalityforadampedhyperbolicequationinonespacedimension AT kenanyildirim necessaryandsufficientconditionsofoptimalityforadampedhyperbolicequationinonespacedimension |