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共分散行列の正実性を考慮した確率的同定問題に関する基礎的研究

Research Project

Project/Area Number 15760316
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Control engineering
Research InstitutionKyoto University

Principal Investigator

田中 秀幸  京都大学, 情報学研究科, 助手 (90303883)

Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords確率実現 / 確率的部分空間同定法 / 正準相関解析 / 確率的平衡実現 / ヒルベルト空 / LQ分解 / リカッチ方程式 / 正実性 / 正準相関解 / ヒルベルト空間
Research Abstract

本年度は,主に異常値が含まれる場合にも対応できるような確率的部分空間同定法を開発し,昨年度より複雑な場合の同定について考察を行った.具体的な研究成果は以下の4通りである.
1)異常値が含まれる場合に対応できるシステム同定を考察した.具体的には,部分空間同定法の結果を初期値としてEMアルゴリズムによって推定値を改善する方法を考察し,システム制御情報学会論文誌に投稿した結果採用された(2005年5月号).また,異常値が含まれる場合の確率的部分空間同定法として,直交射影を繰り返す方法(査読のある国際学会CDC-ECC'05)とLeave-k-outによって異常値を検出する方法を開発した(査読のある学会SICE2005).
2)これまで確率実現に基づいて提案した方法をまとめ,Automaticaに投稿した結果,2006年5月号に採用予定である.また,確率的部分空間同定法をまとめ提案法の利点を明らかにした(査読のある国際会議IFAC2005).
3)これまでの知識を生かして閉ループ同定について考察を行った(査読のある国際学会IFAC2005).
4)共分散行列の正実性に冠する研究結果を非正実な問題へと拡張して時期テーマとすべく,周波数データを用いて変数誤差モデルの同定に関する研究を行った.この予備的な研究は2006年3月下旬に開催される査読のある国際学会SYSID 2006に投稿して,採用された.
なお,3年間の科研費助成による本研究の成果を何件か海外発表したことにより,2006年9月にポルトガルで行われるControlo 2006年の部分空間同定法のオーガナイズドセッションに招待された(投稿中).また,本研究の知識を生かした研究として,非線形性を含む場合や周波数領域のデータを使う研究を学生との共同の研究で行うことができた.

Report

(3 results)
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (17 results)

All 2006 2005 2004 Other

All Journal Article (12 results) Publications (5 results)

  • [Journal Article] A stochastic realization algorithm via block LQ decomposition in Hilbert space2006

    • Author(s)
      H.Tanaka, T.Katayama
    • Journal Title

      Automatica Vol.42・No.5(to appear)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Identification of dynamic errors-in-variables mode s from discrete time frequency domain power spectra2006

    • Author(s)
      H.Tanaka, T.Katayama
    • Journal Title

      Preprints of the 14th IFAC Symposium on System Identification (SYSID2006)

      Pages: 202-207

    • Related Report
      2005 Annual Research Report
  • [Journal Article] EM Algorithm for state-space identification with observation outliers --- an initialization by subspace methods2005

    • Author(s)
      J.ALMutawa, H.Tanaka, T.Katayama
    • Journal Title

      Transaction of the Institute of Systems, Control and Information Engineers (システム制御情報学会論文誌) Vol.18.No.5

      Pages: 178-186

    • NAID

      10015707736

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Stochastic subspace identification guaranteeing stability and minimum phase2005

    • Author(s)
      H.Tanaka, T.Katayama
    • Journal Title

      Preprints of the 16th IFAC World Congress in Prague, Czech Republic (IFAC2005)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A simple subspace identification method of closed-loop systems using orthogonal decomposition2005

    • Author(s)
      T.Katayama, H.Tanaka, T.Enomoto
    • Journal Title

      Preprints of the 16th IFAC World Congress in Prague, Czech Republic (IFAC2005)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Stochastic subspace identification of linear systems with observation outliers2005

    • Author(s)
      H.Tanaka, J.ALMutawa, Katayama
    • Journal Title

      Proc. of the 44th IEEE Conference on Decision and Control and the European Control Conference 2005 (CDC-ECC'05)

      Pages: 7090-7095

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Stochastic subspace identification with observation outliers using leave-k-out diagnostics2005

    • Author(s)
      J.ALMutawa, H.Tanaka, T.Katayama
    • Journal Title

      Proc. of the SICE Annual Conference 2005 in Okayama, Okayama University, Okayama, Japan

      Pages: 3412-3417

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On a stochastic subspace identification algorithm via a block LQ decomposition2005

    • Author(s)
      H.Tanaka, T.Katayama
    • Journal Title

      Proc.of the 36th ISCIE Int.Symp.Stochastic Systems Theory and its Applications, Tokyo Denki University (SSS04) (to appear)(印刷中)

    • NAID

      130007377072

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stochastic subspace identification guaranteeing stability and minimum phase2005

    • Author(s)
      H.Tanaka, T.Katayama
    • Journal Title

      Proc.of the 16th IFAC world congress in Prague, Czech Republic, (IFAC2005) (to appear)(印刷中)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] EM algorithm for state-space identification with observation outliers -An initialization by subspace methods2005

    • Author(s)
      J.ALMutawa, H.Tanaka, T.Katayama
    • Journal Title

      Trans.Institute Systems, Control & Information Engineers (to appear)(印刷中)

    • NAID

      10015707736

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A simple subspace identification method of closed-loop systems using orthogonal decomposition2005

    • Author(s)
      T.Katayama, H.Tanaka, T.Enomoto
    • Journal Title

      Proc.of the 16th IFAC world congress in Prague, Czech Republic, (IFAC2005) (to appear)(印刷中)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A stochastically balanced realization on a finite-interval2004

    • Author(s)
      H.Tanaka, T.Katayama
    • Journal Title

      Proc.of the 16th International symposium on mathematical theory (MTNS2004) (CDROM収録)

    • Related Report
      2004 Annual Research Report
  • [Publications] H.Tanaka, T.Katayama: "A stochastic realization in a Hilbert space based on "LQ decomposition" with application to subspace identification"Proc.of the 13th IFAC Symposium on System Identification, (SYSID2003). 899-904 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Tanaka, T.Katayama: "A stochastic realization on a finite interval via "LQ decomposition" in Hilbert space"Proc.of European Control Conference (ECC2003). (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Tanaka, T.Katayama: "Stochastic subspace identification via "LQ decomposition""Proc of the 42nd IEEE Conference on Decision and Control (CDC2003). 3467-3472 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Tanaka, J.ALMutawa, T.Katayama: "Subspace Identification of Linear Systems with Observation Outliers (出力に異常雑音を含む線形システムの部分空間同定法)"システム制御情報学会論文誌. 17巻・2号. 89-96 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] J.ALMutawa, H.Tanaka, T.Katayama: "EM Algorithm for System Identification in the presence of Outliers"Proc.of the 35th ISCIE International Symposium on Stochastic Systems Theory and Its Applications, Ube, Japan (SSS2003). (to appear). (2004)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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