The Cost Functional and Its Gradient in Optimal Boundary Control Problem for Parabolic Systems
The Cost Functional and Its Gradient in Optimal Boundary Control Problem for Parabolic Systems作者机构：CS Department College of Computers and IT Taif University Taif KSA Department of Mathematics Faculty of Science Fayoum University Fayoum Egypt Mathematics Department Faculty of Science Taif University Taif KSA
出 版 物：《Open Journal of Optimization》 (最优化（英文）)
年 卷 期：2017年第6卷第1期
页 面：26-37页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Constrained Optimal Control Problems Necessary Optimality Conditions Parabolic System Adjoint Problem Exterior Penalty Function Method Existence and Uniqueness Theorems
摘 要：The problems of optimal control (OCPs) related to PDEs are a very active area of research. These problems deal with the processes of mechanical engineering, heat aeronautics, physics, hydro and gas dynamics, the physics of plasma and other real life problems. In this paper, we deal with a class of the constrained OCP for parabolic systems. It is converted to new unconstrained OCP by adding a penalty function to the cost functional. The existence solution of the considering system of parabolic optimal control problem (POCP) is introduced. In this way, the uniqueness theorem for the solving POCP is introduced. Therefore, a theorem for the sufficient differentiability conditions has been proved.
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