The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints
This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad
2022-07-01
|
| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/2816 |
| _version_ | 1811320312161107968 |
|---|---|
| author | jamil Amir Al-Hawasy Wissam A. Abdul-Hussien Al-Anbaki |
| author_facet | jamil Amir Al-Hawasy Wissam A. Abdul-Hussien Al-Anbaki |
| author_sort | jamil Amir Al-Hawasy |
| collection | DOAJ |
| description |
This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint equations is obtained. Lastly, both the necessary conditions for optimality and sufficient conditions for optimality of the proposed problem are stated and proved. The derivation for the Fréchet derivative of the Hamiltonian is attained.
|
| first_indexed | 2024-04-13T12:57:35Z |
| format | Article |
| id | doaj.art-4990be3153844966a79ae35819a4f642 |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-04-13T12:57:35Z |
| publishDate | 2022-07-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-4990be3153844966a79ae35819a4f6422022-12-22T02:46:00ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072022-07-0135310.30526/35.3.2816The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraintsjamil Amir Al-Hawasy0Wissam A. Abdul-Hussien Al-Anbaki1Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq.Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq. This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint equations is obtained. Lastly, both the necessary conditions for optimality and sufficient conditions for optimality of the proposed problem are stated and proved. The derivation for the Fréchet derivative of the Hamiltonian is attained. https://jih.uobaghdad.edu.iq/index.php/j/article/view/2816Quaternary Classical Optimal Control, Quaternary Nonlinear Parabolic Boundary Value Problems, Necessary and Sufficient for Optimality Theorems |
| spellingShingle | jamil Amir Al-Hawasy Wissam A. Abdul-Hussien Al-Anbaki The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints Ibn Al-Haitham Journal for Pure and Applied Sciences Quaternary Classical Optimal Control, Quaternary Nonlinear Parabolic Boundary Value Problems, Necessary and Sufficient for Optimality Theorems |
| title | The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints |
| title_full | The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints |
| title_fullStr | The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints |
| title_full_unstemmed | The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints |
| title_short | The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints |
| title_sort | classical continuous optimal control for quaternary nonlinear parabolic boundary value problems with state vector constraints |
| topic | Quaternary Classical Optimal Control, Quaternary Nonlinear Parabolic Boundary Value Problems, Necessary and Sufficient for Optimality Theorems |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/2816 |
| work_keys_str_mv | AT jamilamiralhawasy theclassicalcontinuousoptimalcontrolforquaternarynonlinearparabolicboundaryvalueproblemswithstatevectorconstraints AT wissamaabdulhussienalanbaki theclassicalcontinuousoptimalcontrolforquaternarynonlinearparabolicboundaryvalueproblemswithstatevectorconstraints AT jamilamiralhawasy classicalcontinuousoptimalcontrolforquaternarynonlinearparabolicboundaryvalueproblemswithstatevectorconstraints AT wissamaabdulhussienalanbaki classicalcontinuousoptimalcontrolforquaternarynonlinearparabolicboundaryvalueproblemswithstatevectorconstraints |