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Error Bound and Performance Guarantee for Nonlinear Control: Application of Validated Numerical Computation and Sum-of-Squares Polynomials

Research Project

Project/Area Number 15K06157
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Control engineering/System engineering
Research InstitutionNanzan University

Principal Investigator

OISHI Yasuaki  南山大学, 理工学部, 教授 (80272392)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords非線形システム / サンプル値制御 / 最適制御 / 精度保証つき数値計算 / 2乗和多項式 / 安定多様体法 / 平均ベクトル場法 / 射撃法 / Hamilton系 / 蓄電池 / 太陽光発電 / 電力買い取り / サンプル時刻間性能 / 楕円制限三体問題 / 周期的システム / 離散化 / 擬似線形表現 / パラメータ依存線形行列不等式 / コントロールモーメントジャイロスコープ
Outline of Final Research Achievements

For sampled-data control and optimal control of a nonlinear system, new methodology is developed with numerical computational techniques and optimization techniques. First, in order to design a sampled-data controller for a nonlinear system with performance guarantee, it is proposed to discretize a given nonlinear system with an error bound and to design a robust controller. This is realized with the techniques of validated numerical computation and sum-of-squares polynomials. Also, for improvement of the stable-manifold method, which is a promising method for nonlinear optimal control, it is proposed to introduce the mean-vector-field method for trajectory computation of the associated Hamiltonian system and to develop a shooting method for systematic choice of an initial point of the trajectory. Moreover, application of nonlinear control and optimal control is considered to practical systems.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (17 results)

All 2018 2017 2016 2015 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results,  Open Access: 3 results,  Acknowledgement Compliant: 3 results) Presentation (9 results) Remarks (2 results)

  • [Journal Article] Maintenance of the Halo Orbit for a Spacecraft Using Discrete-time Optimal Control2018

    • Author(s)
      坂井祐介,宇佐美元啓,大石泰章
    • Journal Title

      Transactions of the Society of Instrument and Control Engineers

      Volume: 54 Issue: 2 Pages: 247-252

    • DOI

      10.9746/sicetr.54.247

    • NAID

      130006386578

    • ISSN
      0453-4654, 1883-8189
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Numerical computational improvement of the stable-manifold method2017

    • Author(s)
      Yasuaki Oishi and Noboru Sakamoto
    • Journal Title

      Proceedings of the 20th IFAC World Congress

      Volume: - Issue: 1 Pages: 5264-5269

    • DOI

      10.1016/j.ifacol.2017.08.777

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Design of a Dynamic Quantizer for a Nonlinear System2016

    • Author(s)
      荒川紘次,大石泰章
    • Journal Title

      Transactions of the Society of Instrument and Control Engineers

      Volume: 52 Issue: 2 Pages: 53-59

    • DOI

      10.9746/sicetr.52.53

    • NAID

      130005126503

    • ISSN
      0453-4654, 1883-8189
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Validated discretization of a nonlinear system: Extension for a nonpolynomial system and intersample performance2016

    • Author(s)
      Yasuaki Oishi
    • Journal Title

      Proceedings of the SICE International Symposium on Control Systems 2016

      Volume: 1

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Robustification of a Nonlinear Dynamical System with a Stability Index and a Matrix Inequality2015

    • Author(s)
      Oishi Yasuaki, Mio Kobayashi and Tetsuya Yoshinaga
    • Journal Title

      SICE Journal of Control, Measurement, and System Integration

      Volume: 8:3 Issue: 3 Pages: 209-213

    • DOI

      10.9746/jcmsi.8.209

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Validated discretization and robust controller design for nonlinear sampled-data control2015

    • Author(s)
      Yasuaki Oishi
    • Journal Title

      Proceedings of the 54th IEEE Conference on Decision and Control

      Volume: 1 Pages: 7280-7285

    • DOI

      10.1109/cdc.2015.7403368

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 安定多様体法における射撃法とその応用2018

    • Author(s)
      中村拓登,大石泰章,坂本登
    • Organizer
      第5回計測自動制御学会制御部門マルチシンポジウム
    • Related Report
      2017 Annual Research Report
  • [Presentation] 非線形最適制御における数値計算技術の利用2017

    • Author(s)
      大石泰章,坂本登
    • Organizer
      第4回計測自動制御学会制御部門マルチシンポジウム
    • Place of Presentation
      岡山大学(岡山県岡山市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Research-status Report
  • [Presentation] 離散時間最適制御によるハロー軌道維持:楕円制限三体問題の場合2017

    • Author(s)
      坂井祐介,大石泰章
    • Organizer
      第4回計測自動制御学会制御部門マルチシンポジウム
    • Place of Presentation
      岡山大学(岡山県岡山市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Research-status Report
  • [Presentation] 2乗和多項式に基づくセミアクティブサスペンションの非線形制御2017

    • Author(s)
      松岡浩司,大石泰章
    • Organizer
      第4回計測自動制御学会制御部門マルチシンポジウム
    • Place of Presentation
      岡山大学(岡山県岡山市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Research-status Report
  • [Presentation] 家庭用蓄電池の最適運用とそのロバスト性2017

    • Author(s)
      岩田拓海,大石泰章
    • Organizer
      第61回システム制御情報学会研究発表講演会
    • Related Report
      2017 Annual Research Report
  • [Presentation] クレーンの障害物回避のための軌道生成と軌道追従2016

    • Author(s)
      林達也,伊藤大智,大石泰章
    • Organizer
      第60 回システム制御情報学会研究発表講演会
    • Place of Presentation
      京都テルサ(京都府京都市)
    • Year and Date
      2016-05-25
    • Related Report
      2016 Research-status Report
  • [Presentation] 発散度合いを考慮したハロー軌道の維持制御:連続入力の場合とパルス入力の場合2016

    • Author(s)
      坂井祐介,宇佐美元啓,大石泰章
    • Organizer
      第3回計測自動制御学会制御部門マルチシンポジウム
    • Place of Presentation
      南山大学(愛知県名古屋市)
    • Year and Date
      2016-03-07
    • Related Report
      2015 Research-status Report
  • [Presentation] 閉軌道の繰り返しを用いたControl Moment Gyroscopeの姿勢制御2016

    • Author(s)
      佐野椋一,大石泰章
    • Organizer
      第3回計測自動制御学会制御部門マルチシンポジウム
    • Place of Presentation
      南山大学(愛知県名古屋市)
    • Year and Date
      2016-03-07
    • Related Report
      2015 Research-status Report
  • [Presentation] 地球-月系円制限三体問題におけるハロー軌道の維持制御2015

    • Author(s)
      宇佐美元啓,坂井祐介,大石泰章
    • Organizer
      第58回自動制御連合講演会
    • Place of Presentation
      神戸大学(兵庫県神戸市)
    • Year and Date
      2015-11-14
    • Related Report
      2015 Research-status Report
  • [Remarks] 学術論文および学会発表

    • URL

      http://www.st.nanzan-u.ac.jp/info/oishi/papers-j.html

    • Related Report
      2017 Annual Research Report 2016 Research-status Report
  • [Remarks] 学術論文および学会発表

    • URL

      http://www.seto.nanzan-u.ac.jp/~oishi/papers-j.html

    • Related Report
      2015 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2019-03-29  

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