Construction of the stabilization theory in the delayed feedback control and its applications

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04953
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Shizuoka University
• Principal Investigator: Miyazaki Rinko 静岡大学, 工学部, 教授 (40244660)
• Co-Investigator(Kenkyū-buntansha): 泰中 啓一 静岡大学, 創造科学技術大学院, 客員教授 (30142227) ; 内藤 敏機 電気通信大学, その他部局等, 名誉教授 (60004446)
• Research Collaborator: SHIN Jong Son 法政大学, 非常勤講師
• Project Period (FY): 2015-10-21 – 2018-03-31
• Keywords: 遅延型微分方程式 / 関数方程式 / 周期系 / 安定性 / 制御

Outline of Final Research Achievements

For the purpose of construction of the theoretical framework of the delayed feedback control method, we engaged two themes, relaxing the restrictions to the gain in our results in 2011 and the analysis of the case which includes errors in the delay. Although we had not obtained the perfect solution, we could three new results. (1) We prove that Echo type of DF control which is a delayed feedback control with 1 advanced step time is effective. (2) We prove the necessary and sufficient condition of the Floquet multipliers of the periodic solution for DF control to be successful. (3) We prove that the existence of periodic solutions of nonhomogeneous linear systems generated from a periodic evolutionary process.

Free Research Field

関数微分方程式論