The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints
| Autor: | jamil Amir Al-Hawasy, Wissam A. Abdul-Hussien Al-Anbaki |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Ibn Al-Haitham Journal for Pure and Applied Sciences, Vol 35, Iss 3 (2022) |
| Druh dokumentu: | article |
| ISSN: | 1609-4042 2521-3407 |
| DOI: | 10.30526/35.3.2816 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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