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Optimal Control Theory of Enler-BernouIIi Equation

Research Project

Project/Area Number 12640154
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionSaitama University

Principal Investigator

TSUJIOKA Kunio  Professor, Department of Mathematics, Saitama University, 理学部, 教授 (30012412)

Co-Investigator(Kenkyū-buntansha) KOIKE Shigeaki  Professor, Department of Mathematics, Saitama University, 理学部, 教授 (90205295)
NAGASE Masayoshi  Professor, Department of Mathematics, Saitama University, 理学部, 教授 (30175509)
YANO Tamaki  Professor, Department of Mathematics, Saitama University, 理学部, 教授 (10111410)
SAKURAI Tsutomu  Associate Professor, Department of Mathematics, Saitama University, 理学部, 助教授 (40187084)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
Keywordscontrollability / Euler-Bernoulli equation / singular boundary condition / wave equation / optimal control theory / viscositv solution / Hamilton-Jacobi equation / variational equation / 発展方程式 / 有限伝播速度 / 梁の方程式 / 数理ファイナンス / 近似可制御性 / オイラー・ビーム / Kuhn-Tucker / 多目的制御問題 / モーメント問題 / 最短到達時間問題 / 微分ゲーム / 最適化
Research Abstract

(1) In the first year of the term of the project, the head investigator researched controllability of a system coupled by two Euler- Bernoulli beams with control at the coupled point. First he studied asymptotic behavior of eigenvalues of a fourth order differential operator related to the Euler-BernouIIi equation. Then controllability problem is reduced a moment problem in a Hilbert space. The method to solve controllability by reducing to a moment problem is called moment problem method. Our ultimate object of the project is to study controllability of a system coupled several Euler-Bernoulli beams. However corresponding moment problem method is too complicated and does not work to our problem. So this problem is still open. In the second and third year of the term of the project, he turned to controllability of evolution equations with singular boundary condition. A boundary condition in an evolution equation is called singular if its order in spatial derivative is as same as that of the equation. We investigated controllability of wave equation with singular boundary condition using moment problem method. A. similar result will be obtained for Euler-Bernoulli equation with singular boundary condition.
(2) Investigator Koike contributed greatly to optimal control theory related to viscosity solution. Various problems are proposed and solved by him.

Report

(4 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (19 results)

All Other

All Publications (19 results)

  • [Publications] K.Tsujioka, Y.-S.Shao: "On properefficiency for nonsmooth multiobjective optimal control problems"Bulltin of Informatics and Cybernetics. 32・2. 139-155 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Tsujioka, J.Uchiumi: "Approximate controllability of a system coupled by Euler-Bernoulli beams"Advances in Mathematical Science and Applications. 12・2. 645-663 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Nagase: "The adiabatic limits signature operator for Spin^q manifolds"Osaka Journal of Mathematics. 38. 541-564 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Nagase: "Twister spaces and the adiabatic limits of Dirac operators"Nagoya Mathematical Journal. 164. 53-73 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Koike, H.Morimoto: "Optimal consumption and portofolio choice with stopping"Journal of Mathematical Analysis and Applications.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Koike, H.Morimoto: "On variational inequalities for leavable boundary-velocity control"Applied Mathematics and Optimization.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Tsujioka, Y.-S..Shao: "On Proper-Efficiency for nonsmooth multiobjective optimal control problems"Bulitine of Informatics. 30. No 2.302. 139-155 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Tsujioka, J.Uchiumi: "Approximate controllability of a system coupled by Euler-Bernoulli beam"Advances in Mathematical Science and Applications. 12, No.2. 645-663 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Nagase: "The adiabatic limits of signature for Spin q"Osaka Journal of Mathematics. 38. 541-564 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Nagase: "Twister spaces and the adiabatic Iinits of Dirac operators"Nagoya Mathematical Journal. 164. 53-73 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Koike, H.Morimoto: "Optimal consumption and Profolio choice with stop"Journal of Mathematical Analysis and Applications. to appeart.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S Koike, H.Morimoto: "On variational inequalities for leavable boundary-velocity control"Applied Mathematics and Optimization. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Koike, H.Morimoto: "Optimal consumption and portofolio choice with stopping"Journal of Mathematical Analysis and Applications.

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Koike, H.Morimoto: "On variational inequalities for leavable boundary-velocity control"Applied mathematics and optimization. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Shao, K.Tsujioka: "On proper-efficiency for nonsmooth multiobjective optimal control problems"Bulletin of Information and Cybernetics. 32・2. 139-155 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] K.Tsujioka, J.Uchiumi: "Approximati controllabiity of a system coupled by Euler-Bernoulli beams"Adrancer in Mathematical Sciences and Applications. 12・2. (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.Koike,O.Alvarez,I.Nakayama: "Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem"SIAM Journal on Control and Optimization. 38・2. 470-481 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Koike,M.Bardi,P.Soravia: "Pursuit-evasion games with state constraints dynamic programming and discrete-time approximations"Discrete and Continuous Dynamical Systems. 6・2. 361-380 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Koike,H.Ishii: "On ε-optimal controls for state constraint problems"Annales de l'Institut Henri Poincare, Analyses Non Lineaire. 17・4. 473-502 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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