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Construction and Implementation of Stochastic Nash Equilibrium for Large-Scale Systems with Noise

Research Project

Project/Area Number 20500014
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionHiroshima University

Principal Investigator

MUKAIDANI Hiroaki  Hiroshima University, 大学院・教育学研究科, 准教授 (70305788)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsナッシュ均衡 / 確率微分方程式 / リカッチ方程式 / 動的ナッシュゲーム / 大規模システム / パレート最適 / 伊藤確率微分方程式 / 動的ゲーム / 離散時間システム / コスト保証制御 / 連立型確率Riccati方程式 / 指数平均二乗安定 / 出力フィードバック
Research Abstract

In this study, the Nash equilibrium problem for a class of large-scale uncertain systems has been addressed. After describing the uncertainties by means of Ito differential equation, in order to attain the stochastic Nash equilibrium and to obtain the strategy set some conditions and numerical algorithms have been established. As compared with the existing results, even if there exist the modeling errors and the uncertainty due to the variation of environment, it has been shown that the Nash equilibrium strategy can be designed. Moreover, the proposed methodology has been confirmed via the numerical simulation.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (32 results)

All 2011 2010 2009 2008 Other

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (17 results) Remarks (1 results)

  • [Journal Article] 弱結合大規模マルコフジャンプ確率システムのためのナッシュゲーム2011

    • Author(s)
      相良宗臣, 向谷博明
    • Journal Title

      電気学会論文誌C Vol.131-C, No.3

      Pages: 644-654

    • NAID

      10027804553

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 弱結合大規模マルコフジャンプ確率システムのためのナッシュゲーム2011

    • Author(s)
      相良宗臣, 向谷博明
    • Journal Title

      電気学会論文誌C

      Volume: 131-C Pages: 644-654

    • NAID

      10027804553

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic Optimal Control for Weakly Coupled Large-Scale Systems via State and Static Output Feedback2010

    • Author(s)
      Hiroaki Mukaidani, Hua Xu, Vasile Dragan
    • Journal Title

      IET Control Theory & Applications Vol.4, Iss.9

      Pages: 1849-1858

    • NAID

      120002737843

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 離散時間弱結合大規模確率システムにおける動的ゲームの特徴2010

    • Author(s)
      Hiroaki Mukaidani, Hua Xu
    • Journal Title

      計測自動制御学会論文集 Vol.46, No.8

      Pages: 501-510

    • NAID

      10026585654

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 離散時間弱結合大規模確率システムにおける動的ゲームの特徴2010

    • Author(s)
      向谷博明, Hua Xu
    • Journal Title

      計測自動制御学会論文集

      Volume: 46 Pages: 501-510

    • NAID

      10026585654

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic Optimal Control for Weakly Coupled Large-Scale Systems via State and Static Output Feedback2010

    • Author(s)
      H.Mukaidani, H.Xu, V.Dragan
    • Journal Title

      IET Control Theory & Applications

      Volume: 4 Pages: 1849-1858

    • NAID

      120002737843

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Near-Optimal Control for Singularly Perturbed Stochastic Systems2009

    • Author(s)
      Muneomi Sagara, Hiroaki Mukaidani, Toru Yamamoto
    • Journal Title

      IEICE Trans. Vol.E92-A, No.11

      Pages: 2874-2882

    • NAID

      10026861040

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 動的ゲーム理論とロバスト性2009

    • Author(s)
      向谷博明
    • Journal Title

      計測と制御 Vol.48, No.9

      Pages: 718-723

    • NAID

      10025524401

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pareto Optimal Strategy for Stochastic Weakly Coupled Large Scale Systems with State Dependent System Noise2009

    • Author(s)
      Hiroaki Mukaidani, Hua Xu
    • Journal Title

      IEEE Trans. Automatic Control Vol.54, No.9

      Pages: 2244-2250

    • NAID

      120001898376

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Robust Guaranteed Cost Control for Uncertain Stochastic Systems with Multiple Decision Makers2009

    • Author(s)
      向谷博明
    • Journal Title

      Automatica Vol.45, No.7

      Pages: 1758-1764

    • NAID

      120001255523

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Soft-Constrained Stochastic Nash Games for Weakly Coupled Large-Scale Systems2009

    • Author(s)
      向谷博明
    • Journal Title

      Automatica Vol.45, No.5

      Pages: 1272-1279

    • NAID

      120001255524

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pareto Optimal Strategy for Stochastic Weakly Coupled Large Scale Systems with State Dependent System Noise2009

    • Author(s)
      Hiroaki Mukaidani
    • Journal Title

      IEEE Transactions on Automatic Control VOL.54

      Pages: 2244-2250

    • NAID

      120001898376

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Robust Guaranteed Cost Control for Uncertain Stochastic Systems with Multiple Decision Makers2009

    • Author(s)
      Hiroaki Mukaidani
    • Journal Title

      Automatica VOL.45

      Pages: 1758-1764

    • NAID

      120001255523

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Robust Guaranteed Cost Control for Uncertain stochastic Systems with Multiple Decision Makers

    • Author(s)
      Hiroaki Mukaidani
    • Journal Title

      Automatica (印刷中)

    • NAID

      120001255523

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] A Numerical Computation of Linear Quadratic Dynamic Games for Stochastic Systems with State- and Control-Dependent Noise2010

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      49th IEEE Conference on Decision and Control, pp.4126-4131
    • Place of Presentation
      Atlanta, Georgia, USA.
    • Year and Date
      2010-12-16
    • Related Report
      2010 Final Research Report
  • [Presentation] Stochastic Nash Games for Weakly Coupled Large Scale Discrete-Time Systems with State- and Control-Dependent Noise2010

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      49th IEEE Conference on Decision and Control, pp.1429-1435
    • Place of Presentation
      Atlanta, Georgia, USA.
    • Year and Date
      2010-12-15
    • Related Report
      2010 Final Research Report
  • [Presentation] A Numerical Computation of Linear Quadratic Dynamic Games for Stochastic Systems with State- and Control-Dependent Noise2010

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      49th IEEE Conference on Decision and Control
    • Place of Presentation
      Atlanta, Georgia, USA
    • Year and Date
      2010-12-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stochastic Nash Games for Weakly Coupled Large Scale Discrete-Time Systems with State- and Control-Dependent Noise2010

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      49th IEEE Conference on Decision and Control
    • Place of Presentation
      Atlanta, Georgia, USA
    • Year and Date
      2010-12-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] An Approximate Pareto Strategy Design for Weakly Coupled Large Scale Discrete-Time Systems with State- and Control-Dependent Noise2010

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      IEEE Multi-conference on Systems and Control, pp.761-766
    • Place of Presentation
      Yokohama, Japan.
    • Year and Date
      2010-09-08
    • Related Report
      2010 Final Research Report
  • [Presentation] Static Output Feedback Strategy of Stochastic Nash Games for Weakly-Coupled Large-Scale Systems2010

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      2010 American Control Conference, pp.361-366
    • Place of Presentation
      Baltimore, Maryland, USA.
    • Year and Date
      2010-06-30
    • Related Report
      2010 Final Research Report
  • [Presentation] Soft-Constrained Stochastic Nash Games for Multimodeling Systems via Static Output Feedback Strategy2009

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      48th IEEE Conference on Decision and Control, pp.5786-5791
    • Place of Presentation
      Shanghai, PRC.
    • Year and Date
      2009-12-17
    • Related Report
      2010 Final Research Report
  • [Presentation] Guaranteed Cost Control for Uncertain Stochastic Systems with Multiple Decision Makers via Static Output Feedback2009

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      48th IEEE Conference on Decision and Control, pp.2917-2922
    • Place of Presentation
      Shanghai, PRC.
    • Year and Date
      2009-12-16
    • Related Report
      2010 Final Research Report
  • [Presentation] Soft-Constrained Stochastic Nash Games for Multimodeling Systems via Static Output Feedback Strategy2009

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      48th IEEE Conference on Decision and Control
    • Place of Presentation
      Shanghai, P. R. China
    • Year and Date
      2009-12-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] Guaranteed Cost Control for Uncertain Stochastic Systems with Multiple Decision Makers via Static Output Feedback2009

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      48th IEEE Conference on Decision and Control
    • Place of Presentation
      Shanghai, P. R. China
    • Year and Date
      2009-12-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] Decentralized Stochastic Guaranteed Cost Control for Uncertain Nonlinear Large-scale Interconnected Systems under Gain Perturbations2009

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      2009 American Control Conference, pp.5097-5102
    • Place of Presentation
      St. Louis, Missouri, USA.
    • Year and Date
      2009-06-12
    • Related Report
      2010 Final Research Report
  • [Presentation] Stochastic Nash Games for Multimodeling Systems2009

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      2009 American Control Conference, pp.4404-4409
    • Place of Presentation
      St. Louis, Missouri, USA.
    • Year and Date
      2009-06-12
    • Related Report
      2010 Final Research Report
  • [Presentation] Stochastic H_∞ Control Problem with State-Dependent Noise for Multimodeling Systems2009

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      2009 American Control Conference, pp.4410-4415
    • Place of Presentation
      St. Louis, Missouri, USA.
    • Year and Date
      2009-06-12
    • Related Report
      2010 Final Research Report
  • [Presentation] Stochastic Pareto Near-Optimal Strategy for Weakly-Coupled Large-Scale Systems with Imperfect Local state Measurements2008

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      47th IEEE Conference on Decision and Control
    • Place of Presentation
      Cancun, Mexico
    • Year and Date
      2008-12-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Stochastic Pareto Near-Optimal Strategy for Weakly-Coupled Large-Scale Systems with Imperfect Local State Measurements2008

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      47th IEEE Conference on Decision and Control, pp.4293-4299
    • Place of Presentation
      Cancun, Mexico.
    • Year and Date
      2008-12-10
    • Related Report
      2010 Final Research Report
  • [Presentation] Infinite-Horizon Soft-Constrained Stochastic Nash Games with State-Dependent Noise in Weakly Coupled Large-Scale Systems2008

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      2008 American Control Conference, pp.4232-4237
    • Place of Presentation
      Seattle, USA.
    • Year and Date
      2008-06-13
    • Related Report
      2010 Final Research Report
  • [Presentation] Recursive Computation of Stochastic Nash Games with State-Dependent Noise for Weakly-Coupled Large-Scale Systems2008

    • Author(s)
      Hiroaki Mukaidani
    • Organizer
      2008 American Control Conference, pp.5016-5022
    • Place of Presentation
      Seattle, USA.
    • Year and Date
      2008-06-13
    • Related Report
      2010 Final Research Report
  • [Remarks] ホームページ等

    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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