Solvability of the Quaternary Continuous Classical Boundary Optimal Control Dominated by Quaternary Parabolic System
DOI:
https://doi.org/10.21123/bsj.2023.8690Keywords:
Adjoint Eqs. , Constraint Continue Classical Optimal Control Vector, Necessary Conditions, Quaternary Nonlinear Parabolic System, Sufficient Condition, The Fréchet DerivativeAbstract
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.
Received 04/03/2023
Revised 01/07/2023
Accepted 03/07/2023
Published Online First 20/11/2023
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