The Cost Functional and Its Gradient in Optimal Boundary Control Problem for Parabolic Systems

• 作者: Fahad B. Al-Thobaiti M. H. Farag Mohamed A. El-Sayed Moustafa M. Salama
• 来源期刊: 最优化(英文)
• 学科: 数学
• 关键词: Constrained Optimal Control Problems Necessary OPTIMALITY Conditions Parabolic System ADJOINT Problem Exterior PENALTY Function Method Existence and Uniqueness THEOREMS
• 年，卷（期）: 2017,（1）
• 页码范围: 26-37
• 页数: 12页
• 分类号: O1

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.