Project/Area Number  10640207 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Global analysis

Research Institution  Kobe University 
Principal Investigator 
NAMBU Takao Kobe University, Faculty of Engineering, Department of Computer & Systems Engineering, professor, 工学部, 教授 (40156013)

CoInvestigator(Kenkyūbuntansha) 
SANO Hideki Kagoshima University, Faculty of Science, Department of Mathematical Scienxes, associate professor, 理学部, 助教授 (70278737)
NAITO Yuki Kobe University, Faculty of Engineering, Department of Computer & Systems Engineering, associate professor, 工学部, 助教授 (10231458)
TABATA Minoru Kobe University, Faculty of Engineering, Department of Computer & Systems Engineering, associate professor, 工学部, 助教授 (70207215)
NAKAGIRI Shinichi Kobe University, Faculty of Engineering, Department of Computer & Systems Engineering, professor, 工学部, 教授 (20031148)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,400,000 (Direct Cost : ¥2,400,000)
Fiscal Year 1999 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  boundary control / algebraic transform / linear parabolic systems / null controllability / HィイD1∞ィエD1control / moving sphere method / population dynamics / dynamic compensator / H^∞control / boundary control systems / feedback control / algebraic method / spectrum assignment / mixed boundary conditions / higher order parabolic systems 
Research Abstract 
1.Stabilization of linear parabolic systems by means of boundary feedback is studied. The boundary condition is partially of the first kind and partially of the third kind. An entirely new and simple algebraic transform (isomorphism in LィイD12ィエD1spaces) is introduced for the complicated boundary condition. By introducing a finitedimensional dynamic compensator of general type, stabilization is achieved for more complicated control systems. An algebraic structure of the so called Silvester equation with unbounded linear operators as coefficients is also studied. 2.Approximate null controllability problem is studied for a class of linear second order parabolic systems in Hilbert spaces by means of the so called HUM method. A numerical approximation of solutions to the sineGordon equation is also studied by means of FEM. 3.An integropartial differential equation is established as a mathematical model for studing logistic growth of human population with migration. It is proven that the C
… More
auchy problem admits the unique global solution in time. The asymptotic behavior of the solutions is also investigated. The property of solutions is used for explaining about the recent change of labor dynamics in European Continent. 4.A class of nonlinear elliptic partial differential equations is studied, where the appearing coefficients and the spatial domain has a kind of symmetry. Existence and uniqueness of solutions are proven via ODE approach. A generalization of the so called moving sphere method is also obtained. 5.Stabilization problem is studied for linear parabolic control systems by means of HィイD1∞ィエD1control method. Robustness of the stabilizing feedback control scheme is proven in some topology. Another stabilization problem is also studied, where the sensors and actuators are periodic functions in time. By generalizing the result of Brunovsky (JDE, 1969), the stabilization is achieved. 6.制御系の外乱に対する堅固さ(robustness)に関連するH^∞制御の概念を考慮した線形放物系安定化を考察し、その十分条件を求めた。また、制御アクチュエータや観測重み関数が時間の周期関数である場合に、上記の安定化問題を、Brunovsky(JDE,1969)の結果を一般化することにより解いた(佐野)。 Less
