21世紀COE「超ロバスト計算原理プロジェクト」最適化/制御 セミナー

投稿日:2005/04/28投稿者:石井秀明
        東京大学工学部計数工学科 システム情報談話会
21世紀COE「超ロバスト計算原理プロジェクト」最適化/制御 セミナー

日時: 5月9日(月) 15:30〜17:00

場所: 東京大学本郷キャンパス 工学部6号館3階 セミナー室A/D

講演者:Jan C. Willems (K.U. Leuven, Belgium)

題目:DISTRIBUTED DISSIPATIVE SYSTEMS

概要:
We will first introduce some basic system theory concepts for systems
described by linear constant coefficient PDE\'s, within the behavioral
framework. Issues as controllability and observability will be briefly
discussed, taking Maxwell\'s equations as a paradigmatic example. We then
turn our attention to dissipative systems. The notion of a dissipative
dynamical system was introduced in the early 1970\'s. It generalizes the
idea of a Lyapunov function to `open\' dynamical systems. This concept
has found  applications in diverse areas of systems and control, for
example, in stability theory, system norm estimation, robust control,
etc. Of particular importance is  the question of construction of a
storage function. It is this problem that brought LMI\'s to the
foreground. The main aim of this talk is the construction of storage
functions for systems described by linear PDE\'s and supply rates that
are quadratic expressions in the system variables and their derivatives.
The construction of a storage function then reduces to factorization of
polynomial matrices in many variables. This leads straight to Hilbert\'s
17-th problem and the sum-of-squares problem.


連絡先:  原辰次     (Shinji_Hara@ipc.i.u-tokyo.ac.jp)
         石井秀明   (Hideaki_Ishii@ipc.i.u-tokyo.ac.jp)