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Quasi Hankel and Relevant Operators together with Their Norm Analysis Aiming at Challenging Control Performance Evaluation

Research Project

Project/Area Number 18K04198
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 21040:Control and system engineering-related
Research InstitutionKyoto University

Principal Investigator

Hagiwara Tomomichi  京都大学, 工学研究科, 教授 (70189463)

Project Period (FY) 2018-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsハンケルノルム / サンプル値系 / 周期時変系 / 準ハンケルノルム / L_∞/L_2誘導ノルム / H2ノルム / L_2/L_2ハンケルノルム / 演算時間遅れ / 動的システム / ハンケル作用素 / 準ハンケル作用素 / 制御性能規範 / 離散時間制御器
Outline of Final Research Achievements

By introducing the notion of quasi Hankel operators, studies on Hankel norm are extended to sampled-data systems and periodic systems. It is studied whether the values of the norms of quasi Hankel operators called the quasi Hankel norms attain their maximum over a single (half-open) interval corresponding to the period of the system. It is also studied how to compute the Hankel norm defined as the supremum of the quasi Hankel norms. The relationship between the quasi Hankel and Hankel operators and the well-known H2 norm is studied, and the discrete-time controller synthesis method for minimizing the L-infinity/L2 Hankel norm is derived.

Academic Significance and Societal Importance of the Research Achievements

現実に存在するシステムの多くは動的システムであり,その出力は過去の入力の影響も受ける.過去の入力が未来の出力に影響する度合いを評価するためにハンケルノルムが用いられるが,ディジタル機器を用いた制御系をはじめ,入出力関係が周期性をもつシステムに対しては,ハンケルノルムに基づく性能評価に関する基本的な問題が未解決であった.本研究では準ハンケル作用素と準ハンケルノルムという概念を導入してそのようなシステムに対して性能評価を可能とし,これまで考えられてこなかった性能指標を導入し,あるいはその指標に基づく望ましい制御系を設計することにもつながる研究を展開しており,理論的,実用的意義がある.

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (8 results)

All 2021 2020 2019 2018

All Journal Article (4 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 4 results) Presentation (4 results) (of which Int'l Joint Research: 3 results)

  • [Journal Article] On Well-Definability of the $L_\infty/L_2$ Hankel Operator and Detection of All the Critical Instants in Sampled-Data Systems2021

    • Author(s)
      T. Hagiwara, A. Inai and J. H. Kim
    • Journal Title

      IET Control Theory & Applications

      Volume: 5 Issue: 5 Pages: 668-682

    • DOI

      10.1049/cth2.12069

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] $L_1$ Optimal Controller Synthesis for Sampled-Data Systems via Piecewise Linear Kernel Approximation2021

    • Author(s)
      J. H. Kim and T. Hagiwara
    • Journal Title

      International Journal of Robust and Nonlinear Control

      Volume: --- Issue: 10 Pages: 4933-4950

    • DOI

      10.1002/rnc.5513

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Computing the $L_\infty$-Induced Norm of LTI Systems: Generalization of Piecewise Quadratic and Cubit Approximations2020

    • Author(s)
      J. H. Kim, Y. W. Choi and T. Hagiwara
    • Journal Title

      IEEE Access

      Volume: 8 Pages: 139868-139880

    • DOI

      10.1109/access.2020.3012253

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The L_infinity/L_2 Hankel Operator/Norm of Sampled-Data Systems2018

    • Author(s)
      T. Hagiwara, A. Inai and J. H. Kim
    • Journal Title

      SIAM Journal on Control and Optimization

      Volume: 56 Issue: 5 Pages: 3685-3707

    • DOI

      10.1137/17m1123146

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Generalization of Piecewise Constant Approximation in the $L_\infty/L_2$ Optimal Control of Sampled-Data Systems2019

    • Author(s)
      J. H. Kim and T. Hagiwara
    • Organizer
      2019 European Control Conference
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Properties of the Quasi $L_2/L_2$ Hankel Norms and the $L_2/L_2$ Hankel Operators of Sampled-Data Systems2019

    • Author(s)
      H. Hara and T. Hagiwara
    • Organizer
      2019 European Control Conference
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] 演算時間遅れを考慮したサンプル値系における$L_2/L_2$準ハンケルノルムの計算法と$L_2/L_2$ハンケル作用素2019

    • Author(s)
      原 洋揮,萩原朋道
    • Organizer
      第62回自動制御連合講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] A Study on the Optimal Controller Synthesis for Minimizing the L_2 Norm of the Response to the Worst-Timing Impulse Disturbance in LTI Sampled-Data Systems2018

    • Author(s)
      J. H. Kim and T. Hagiwara
    • Organizer
      2018 IEEE Conference on Decision and Control
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research

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Published: 2018-04-23   Modified: 2022-01-27  

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