研究会 (2023 年 06 月 28 日)

共催：SICE 九州支部制御理論と応用に関する研究会
共催：科研費基盤研究(B) 「錐計画に基づく再帰型ニューラルネットワークの安定性解析と最適設計」 (JP21H01354)

日時: 6/28(水) 15:30〜17:30　(開場 15:00)

場所: アクロス福岡 602 会議室

講演1: Exploring Robust Structured Static Output Feedback Design
　　　　(Dr. Dimitri Peaucelle, LAAS-CNRS, France; 15:30〜16:30)

講演2: L_p+ Induced Norm Analysis of Linear Systems
　　　　(Prof. Yoshio Ebihara, Kyushu University; 16:30〜17:30）

Flyer

参加者: Dimitri Peaucelle(LAAS), Alberto De Marchi(University of the Bundeswehr Munich),
　　　　永原(広大), 蛯原, Andreas Themelis, 山本, 湯野(以上九大),
　　　　延山, 伊藤, 瀬部(以上九工大), 他学生4名.
　　　　　　　　　　　　　　　　　　　　　　(以上敬称略)

問合せ先: 蛯原義雄 (ebihara[a]ees.kyushu-u.ac.jp)

Abstracts.
1.
Many design problems in control can be recast as the search for
static structured (diagonal) output-feedback gains stabilizing
an augmented and rearranged dynamical plant model. Moreover, in
first approximation that plant may be considered as linear, or
at least, one will usually request the linearized plant to be
stable before considering the more complicated non-linear version.
Because of the approximations leading to the linearized version, the
plant parameters are usually uncertain and time-varying. In the
presentation we discuss the possibility to design such static diagonal
output-feedback gains for uncertain linear systems using a recently
proposed matrix inequality based formulation. As expected for this
hard problem, the methodology does not provide a guaranteed to
succeed result, but provides some interesting promising paths for an
efficient algorithm. If we have time we also mention an adaptive
control strategy for updating (learning) the structured static gains.
2.
In this talk, we focus on the L_p+ (p ∈ [1,∞), p = ∞) induced norms
of continuous-time LTI systems where input signals are restricted
to be nonnegative. This induced norm, called the L_p+ induced
norm, is particularly useful for the stability analysis of nonlinear
feedback systems constructed from linear systems and static
nonlinearities where the nonlinearities provide only nonnegative
signals for the case p = 2. We first revisit our methods for upper
bound computation of the L₂₊ induced norm using copositive
programming. To have deeper understanding on the L_p+ induced
norm, we next analyze the lower bounds of L_p+ induced norm with
respect to the standard L_p induced norm. As the main result, we
show that the L_p+ induced norm of an LTI system cannot be smaller
than the L_p induced norm scaled by 2^(1-p)/p for p ∈ [1, ∞) (scaled by
2⁻¹ for p = ∞). On the other hand, in the case where p = 2, we
further propose a method to compute better (larger) lower bounds for
single-input systems via reduction of the lower bound analysis
problem into a semi-infinite programming problem. The
effectiveness of the lower bound computation method, together with
an upper bound computation method proposed in our preceding
studies, is illustrated by numerical examples.

Last modified: Thu Jun 29 09:32:50 JST 2023