Abstract
The purpose of this paper is to study the solvability of the quaternary continuous classical boundary optimal control vector problem dominated by quaternary nonlinear parabolic boundary value problem with state constraints. The existence theorem for a quaternary continuous classical boundary optimal control vector with equality and inequality state constraints is stated and demonstrated under suitable assumptions. The mathematical formulation of the quaternary adjoint eqs. associated with the quaternary nonlinear parabolic boundary value problem with state constraints is discovered. The Fréchet derivative of the cost function and the constraints functions are derived. The necessary and sufficient theorems (conditions) for optimality of the quaternary continuous classical boundary optimal control vector problem are stated and demonstrated under suitable assumptions.
Keywords
Adjoint Eqs., Constraint Continue Classical Optimal Control Vector, Necessary Conditions, Quaternary Nonlinear Parabolic System, Sufficient Condition, The Fréchet Derivative
Article Type
Article
How to Cite this Article
Al-Hawasy, Jamil A. Ali and Naji, Fetan J.
(2024)
"Solvability of the Quaternary Continuous Classical Boundary Optimal Control Dominated by Quaternary Parabolic System,"
Baghdad Science Journal: Vol. 21:
Iss.
6, Article 17.
DOI: https://doi.org/10.21123/bsj.2023.8690
