Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory. (16th June 2020)

• Record Type: Journal Article
• Authors: Hwang, Jin-soo
• Other Names: Mophou Gisele Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-06-16
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/1859736
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In the present article, we consider a von Kárman equation with long memory. The goal is to study a quadratic cost minimax optimal control problems for the control system governed by the equation. First, we show that the solution map is continuous under a weak assumption on the data. Then, we formulate the minimax optimal control problem. We show the first and twice Fréchet differentiabilities of the nonlinear solution map from a bilinear input term to the weak solution of the equation. With the Fréchet differentiabilities of the control to solution mapping, we prove the uniqueness and existence of an optimal pair and find its necessary optimality condition.