The Continuous Classical Boundary Optimal Control Vector Governing by Triple Linear Partial Differential Equations of Parabolic Type

Ibn Al-Haitham Journal for Pure and Applied Sciences

关键词: Continuous Classical Boundary Optimal Control, Triple Linear Partial Differential Equations, Galerkin Method, Necessary Conditions for Optimality.;   

DOI  :  10.30526/33.3.2478

来源: DOAJ

【 摘 要 】

In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and proved.

【 授权许可】

Unknown