The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints
The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of...
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University of Baghdad, College of Science for Women
2019-12-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4607 |
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| author | Jamil A. Ali Al-Hawasy |
| author_facet | Jamil A. Ali Al-Hawasy |
| author_sort | Jamil A. Ali Al-Hawasy |
| collection | DOAJ |
| description | The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the state constrained problem are stated and proved. |
| format | Article |
| id | doaj-art-b168fea1f4bb4529af467e1978d66d09 |
| institution | DOAJ |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2019-12-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-b168fea1f4bb4529af467e1978d66d092025-08-20T02:51:40ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862019-12-01164(Suppl.)10.21123/bsj.2019.16.4(Suppl.).1064The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality ConstraintsJamil A. Ali Al-HawasyThe paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the state constrained problem are stated and proved.http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4607Classical boundary optimal control, Nonlinear hyperbolic, Necessary, Sufficient conditions |
| spellingShingle | Jamil A. Ali Al-Hawasy The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints مجلة بغداد للعلوم Classical boundary optimal control, Nonlinear hyperbolic, Necessary, Sufficient conditions |
| title | The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints |
| title_full | The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints |
| title_fullStr | The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints |
| title_full_unstemmed | The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints |
| title_short | The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints |
| title_sort | continuous classical boundary optimal control of couple nonlinear hyperbolic boundary value problem with equality and inequality constraints |
| topic | Classical boundary optimal control, Nonlinear hyperbolic, Necessary, Sufficient conditions |
| url | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4607 |
| work_keys_str_mv | AT jamilaalialhawasy thecontinuousclassicalboundaryoptimalcontrolofcouplenonlinearhyperbolicboundaryvalueproblemwithequalityandinequalityconstraints AT jamilaalialhawasy continuousclassicalboundaryoptimalcontrolofcouplenonlinearhyperbolicboundaryvalueproblemwithequalityandinequalityconstraints |