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:2005/04/07投稿者:松井知己
        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: 4月11日(金) 13:00〜15:00

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1 ======================== 

講演者: Chung-Yao Kao (University of Melbourne, Australia)
  
題目: Robust Stability Analysis of Systems with Time-Varying Delays

概要:
It is well-known that the manifestation of time delays in a system
can lead to performance degradation and even destabilization of
the system, and hence time delay robustness has been a long
standing research topic in the systems theory community. While much
research has been done and stability criteria have been derived for
systems with uncertain constant time-delays, the recent emphasis has
been put on the scenario where the time delay is time varying. The
significance of such problems is tied to the recent ample interest in
designing control algorithms for large-scale networked systems.

Most existing results for checking robust stability of systems with
time-varying delays were developed based on the Lyapunov-Razumikhin
method or the Lyapunov-Krasovskii. In contrast to the Lyapunov approach,
we engage this line of research via a frequency-domain approach called
Integral Quadratic Constraint (IQC) Analysis. The advantage of IQC
analysis lies in its flexibility. Using this approach, results can be
obtained to cope with situations in which time-varying delays,
parametric and/or un-modelled dynamical uncertainties, and nonlinear
elements such as saturation, relay, hysteresis appear simultaneously.


==== 講演2 ========================

講演者:Ulf Jonsson (Royal Institute of Technology, Sweden)

題目: Analysis of Feedback Systems with Limit Cycle Oscillation

概要:
Oscillators and limit cycle solutions play a crucial role in many
control systems. Examples can be found in electronics, rhythmic motion
control of mechanical systems, in biology, and in various oscillator
synchronization problems. The design and analysis of such systems
raises a number fundamental questions in systems and control. The
existence, uniqueness, and location of periodic solutions of dynamical
systems as well as the stability and robustness of these solutions are
challenging problems that must be addressed.

This talk is devoted to two analysis problems for limit cycles. The
first problem is the stability and robustness of limit cycles of a
general class of systems on Luri form. We show that stability and
robustness can be verified using certain invertibility conditions on
the linear equations that are obtained when the system is linearized
along the limit cycle. The new criterion reduces to a classical
condition on the characteristic multipliers when we consider a finite
dimensional system which is perturbed by an infinite dimensional
operator. The computation of a robustness margin, i.e., a bound on the
maximally allowed perturbation, is also considered.

The second problem is the study of robust stability of networks of
identical coupled oscillators. We assume that the coupling of the
network is such that the nominal limit cycle of the individual
oscillators is embedded in the network solution. The network is said
to be synchronized when this joint oscillation is stable. We provide
conditions for the system to remain synchronized when the oscillators
are perturbed and no longer identical.

The first part of the talk is based on joint work with A. Megretski.


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)