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1st part: A tutorial of function space approach for control problems

Function space approach is one of the powerful tool to attack control problems and the advantage is found in broader field of control theory such as filtering problem, sampled-data control, time-delay and preview control, and receding horizon control problems. In this talk, we describe the fundamental of functional analysis and illustrate the important class of operators with various type of examples, which are adopted from linear algebra, functional analysis, and control theory of linear systems. The objective of this talk is to explain the important class of linear Operators and provide useful concepts, which has a potential to approach various type Of control problems. 1) Hilbert space: Definition and preliminaries, fundamental property, examples. 2) Linear operators: Preliminaries on linear operators, operator norm, adjoint operator, compact operators (Fredholm operator, Volterra operator), examples. 3) Singular-value and eigenvalue problem for compact operators: Definition of singular-value and eigenvalue, fundamental properties, relation to linear system theory, examples. 4) Finite-horizon LQ control problem: Function space approach to finite-horizon LQ control, illustration of eigenvalue, singular value problems, application to constrained control problem.

Type of Seminar:
Public Seminar
Dr. Akira Kojima Assoc. Prof.
Dept. Electronic Systems Engineering, Tokyo Metropolitan Institute of Technology, Japan and Automatic Control Lab.,CH-8092 Zürich
Jan 18, 2001   16:00 bis 18:00

ETH-Zentrum, ETL K 25, Physikstr. 3, 8006 Zurich
Contact Person:

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Biographical Sketch:
Akira Kojima was born in Shizuoka, Japan, in 1965. He is currently an Associate Professor at Tokyo Metropolitan Institute of Technology (Hino-city, Tokyo) and an Academic Guest at Automatic Control Laboratory, ETH. He received B.S, M.S., and Dr.Eng. degrees in Electrical Engineering from Waseda University, Tokyo, Japan, in 1987, 1989 and 1991 respectively. In April 1991, he joined the Department of Electronic Systems Engineering, Tokyo Metropolitan Institute of Technology. Since April 1997, he has been an Associate Professor at Tokyo Metropolitan Institute of Technology. His research interests include Robust Control, Preview/Predictive Control, and Control Theory for Infinite-dimensional Systems. He received Young authors prize in 1992, Outstanding paper award (Takeda Prize) in 1996 from Society of Instrument and Control Engineers, Japan (SICE) . He is a member of SICE, Institute of Systems, Control and Information Engineers, Japan (ISCIE), and IEEE.