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Detection and realization of high performance motions embedded in the Hamilton-Jacobi equation

Research Project

Project/Area Number 19K04446
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 InstitutionNanzan University

Principal Investigator

Sakamoto Noboru  南山大学, 理工学部, 教授 (00283416)

Co-Investigator(Kenkyū-buntansha) 西田 豪  日本大学, 工学部, 准教授 (80435669)
中島 明  南山大学, 理工学部, 教授 (70377836)
Project Period (FY) 2019-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2019: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords最適制御 / 非線形システム / ハミルトン・ヤコビ方程式 / ハミルトン系 / 不変多様体理論 / ラムダ補題 / 非線形制御 / ターンパイク理論 / スパース最適制御
Outline of Research at the Start

制御対象のもつ運動機能を最大限に引き出すための制御系設計理論を構築する.最適制御理論に現れるハミルトン・ヤコビ方程式(HJE)には,対象が制御された結果の運動情報が埋め込まれていることが研究代表者のこれまでの研究で分かってきた.しかし,これを体系的に活用して実際の制御系設計とその実装を行うには,HJEのより深い数学的理解と,これらを取り出し利用するための数値計算理論が必要である.本研究では,ハミルトン力学理論,動的システム理論などを活用し,このような高機能運動を実現する制御系設計の枠組みを構築する.また,実験検証により有用性を確認する.

Outline of Final Research Achievements

Based on the research on optimal control by the principal investigator of this project, it was conjectured that in Hamilton-Jacobi equations of optimal control, much control information is embedded as to achievable controlled motions as well as the possibility of such control.

Academic Significance and Societal Importance of the Research Achievements

メカトロニクス系の制御において標準的に用いられるAcrobotという体操選手を模擬した装置に対し,制御系の切り替えなしに真下から倒立状態へ一気に振上げかつ安定化する制御に成功した.この成果はこれまでどのような非線形制御理論(かつ実験)の研究者も成功しなかった独自の成果で,例えば宇宙ロボットなどの新しい制御方式へ繋がる可能性のがある.
また,計量経済学で重要なターンパイク理論に対して新しい解析手法を提案することができた.これは,ハミルトン系の輸送問題の一種として考察し動的システム理論のラムダ補題などを用いる新規性の高い成果である.

Report

(4 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (12 results)

All 2021 2020 2019 Other

All Int'l Joint Research (4 results) Journal Article (6 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 6 results) Presentation (1 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results) Remarks (1 results)

  • [Int'l Joint Research] German Aerospace Center (DLR)(ドイツ)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] University of Deusto(スペイン)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] University of Deusto(スペイン)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] University of Deusto(スペイン)

    • Related Report
      2019 Research-status Report
  • [Journal Article] The turnpike property in nonlinear optimal control?A geometric approach2021

    • Author(s)
      Sakamoto Noboru、Zuazua Enrique
    • Journal Title

      Automatica

      Volume: 134 Pages: 109939-109939

    • DOI

      10.1016/j.automatica.2021.109939

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Rotor imbalance suppression by optimal control2021

    • Author(s)
      Gnuffi Matteo、Pighin Dario、Sakamoto Noboru
    • Journal Title

      Optimal Control Applications and Methods

      Volume: 43 Issue: 1 Pages: 213-242

    • DOI

      10.1002/oca.2780

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Control of a Class of Underactuated Systems by Successive Submanifold Stabilization2021

    • Author(s)
      Beck Fabian、Sakamoto Noboru、Ott Christian
    • Journal Title

      IFAC-PapersOnLine

      Volume: 54 Issue: 19 Pages: 352-358

    • DOI

      10.1016/j.ifacol.2021.11.102

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A palm circle task controller of contact juggling for ball-and-plate system with 6-DOF manipulator2021

    • Author(s)
      A. Nakashima, T. Ishiguro, N. Sakamoto
    • Journal Title

      Proceedings of the 60th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE)

      Volume: - Pages: 618-623

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The turnpike property in the maximum hands-off control2020

    • Author(s)
      N. Sakamoto and M. Nagahara
    • Journal Title

      2020 59th IEEE Conference on Decision and Control (CDC)

      Volume: - Pages: 2350-2355

    • DOI

      10.1109/cdc42340.2020.9304306

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] The turnpike property in nonlinear optimal control --- A geometric approach2019

    • Author(s)
      N. Sakamoto, D. Pighin, E. Zuazua
    • Journal Title

      2019 IEEE 58th Conference on Decision and Control (CDC)

      Volume: - Pages: 2422-2427

    • DOI

      10.1109/cdc40024.2019.9028863

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Dynamical system view on nonlinear optimal control analysis and design2020

    • Author(s)
      N. Sakamoto
    • Organizer
      IV Stability and Control Processes Conference in memory of Prof. Vladimir Zubov
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] Dycon Working Package 2

    • URL

      https://www.youtube.com/watch?v=kIcO6k9OiVg

    • Related Report
      2019 Research-status Report

URL: 

Published: 2019-04-18   Modified: 2023-01-30  

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