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Analysis and Control of Synchronization in Coupled Nonlinear Systems with Time-delays

Research Project

Project/Area Number 18560441
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Control engineering
Research InstitutionTokyo Metropolitan University

Principal Investigator

OGUCHI Toshiki  Tokyo Metropolitan University, Graduate School of Science and Engineering, Associate Professor (50295474)

Project Period (FY) 2006 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,660,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥360,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2006: ¥2,100,000 (Direct Cost: ¥2,100,000)
KeywordsControl Engineering / Time-delays / Nonlinear systems / Synchronization / Chaotic systems
Research Abstract

This project has been carried out in two phases.
(a) The first phase was to study on synchronization of two coupled nonlinear systems with time-varying delay. In this phase, we introduced the notion of strict semi-dissipativity and showed the convergence property of coupled systems that each system satisfies the strict semi-passive by using the small gain theorem. By using this result, the bounds of the trajectories can be estimated and then a sufficient condition for synchronization can be derived in the form of Linear Matrix Inequalities (LMIs). In addition, in this phase, we proposed a new configuration of anticipating synchronization with the state observer.
(b) The second phase was to extend the results in the first phase into N coupled systems. First, we derived a necessary condition under which the synchronization error dynamics has the origin as an equilibrium solution. The obtained condition means that the networks must have symmetric structures. Under the condition, we obtained sufficient conditions for synchronization in unidirectional or bidirectional networks of N chaotic systems with time-delay coupling. The synchronization conditions derived in this project are based on the Lyapunov-Krasovskii theorem in combination with the LyapunoVs indirect method. The obtained conditions were verified by numerical simulations.
In this paper we targeted on only complete synchronization of coupled systems and have uncovered a phenomenon of partial synchronization in networks. Therefore the analysis of partial synchronization will be the subject of further research.

Report

(3 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • Research Products

    (38 results)

All 2008 2007 2006

All Journal Article (21 results) (of which Peer Reviewed: 5 results) Presentation (17 results)

  • [Journal Article] Erratum:"Anticipating Synchronization of Chaotic Lure Systems"2008

    • Author(s)
      H.Huijberts, H.Nijmeijer, T.Oguchi
    • Journal Title

      Chaos American Institute of Physics 18-1

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Erratum : "Anticipating Synchronization of Chaotic Lur'e Systems"2008

    • Author(s)
      H. Huijberts, H. Nijmeijer, T. Oguchi
    • Journal Title

      Chaos Vol. 18, No. 1

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Erratum: "Anticipating synchronization of chaotic Lur'e systems"2008

    • Author(s)
      H. Huijberts, H. Nijmeijer, T. Oguchi
    • Journal Title

      Chaos(American Institute of Physics) 18

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Anticipating Synchronization of Chaotic Lure Systems2007

    • Author(s)
      H.Huijberts, H.Nijmeijer, T.Oguchi
    • Journal Title

      Chaos American Institute of Physics 17-1

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Synchronization of coupled nonlinear systems with time-delay2007

    • Author(s)
      T.Yamamoto, T.Oguchi, H.Nijmeijer
    • Journal Title

      Proceedings of European Control Conference 2007 (CD-ROM)

      Pages: 3056-3061

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Synchronizatin in Unidirectional Ring Network ofChaotic Systems with Delay-coupling2007

    • Author(s)
      T.Oguchi, H.Nijmeijer, T.Kniknie
    • Journal Title

      電子情報通信学会技術研究報告 (CD-ROM)

      Pages: 27-32

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Anticipating Synchronization of Chaotic Lur'e Systems2007

    • Author(s)
      H. Huijberts, H. Nijmeijer, T. Oguchi
    • Journal Title

      Chaos Vol. 17, No. 2

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Synchronizatin in Unidirectional Ring Network of Chaotic Systems with Delay-coupling2007

    • Author(s)
      T. Oguchi, H. Nijmeijer, T. Kniknie
    • Journal Title

      IEICE Technical Report Vol. 107, No. 399

      Pages: 27-32

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Synchronization in Unidirectional Ring Network of Chaotic Systems with Delay-coupling2007

    • Author(s)
      T. Oguchi, H. Nijmeijer, T. Kniknie
    • Journal Title

      電子情報通信学会技術研究報告 107-399

      Pages: 27-32

    • NAID

      110006549363

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Synchronization of coupled nonlinear systems with time-delay2007

    • Author(s)
      T. Yamamoto, T. Oguchi, H. Nijmeijer
    • Journal Title

      Proceedings of European Control Conference 2007 (CD-ROM)

      Pages: 3056-3061

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Anticipating synchronization of chaotic Lur'e systems2007

    • Author(s)
      H.J.C.Huijberts, H.Nijmeijer, T.Oguchi
    • Journal Title

      Chaos, American Institute of Physics 17

      Pages: 13117-13117

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Synchronization of coupled nonlinear systems with time-delay2007

    • Author(s)
      T.Yamamoto, T.Oguchi, H.Nijmeijer
    • Journal Title

      Proceedings of European Control Conference 2007 (CD-ROM)(採用決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Synchronization of delay-coupled nonlinear oscillators with symmetric structure2007

    • Author(s)
      T.Yamamoto, T.Oguchi, H.Nijmeijer
    • Journal Title

      第7回計測自動制御学会制御部門大会 (CD-ROM)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 非線形システムの同期に基づく状態予測2006

    • Author(s)
      小口 俊樹, H.Nijmeijer
    • Journal Title

      電子情報通信学会技術研究報告 106

      Pages: 45-48

    • NAID

      110006163533

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] むだ時間を有する拡散結合による非線形システムの同期現象2006

    • Author(s)
      山本 昂, 小口 俊樹, H.Nijmeijer
    • Journal Title

      電子情報通信学会技術研究報告 106

      Pages: 49-52

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] State Prediction of Nonlinear Systems based on Synchronization2006

    • Author(s)
      T. Oguchi, H. Nijmeijer
    • Journal Title

      IEICE Technical Report Vol. 106, No. 413

      Pages: 45-48

    • NAID

      110006163533

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Synchronization of diffusively coupled nonlinear systems with time-delay2006

    • Author(s)
      T. Yamamoto, T. Oguchi, H. Nijmeijer
    • Journal Title

      IEICE Technical Report Vol. 106, No. 413

      Pages: 48-52

    • NAID

      110006163534

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Synchronization of coupled nonlinear systems with time-delay2006

    • Author(s)
      T. Yamamoto, T. Oguchi, H. Nijmeijer
    • Journal Title

      Proceedings of European Control 2007

      Pages: 3056-3061

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 非線形システムの同期に基づく状態予測2006

    • Author(s)
      小口俊樹, H.Nijmeijer
    • Journal Title

      電子情報通信学会 非線形問題研究会 信学技報 106・413

      Pages: 45-48

    • NAID

      110006163533

    • Related Report
      2006 Annual Research Report
  • [Journal Article] むだ時間を有する拡散結合による非線形システムの同期現象2006

    • Author(s)
      山本昂, 小口俊樹, H.Nijmeijer
    • Journal Title

      電子情報通信学会 非線形問題研究会 信学技報 106・413

      Pages: 49-52

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Anticipating Synchronization of Nonlinear Systems with Uncertainties2006

    • Author(s)
      T.Oguchi, H.Nijmeijer
    • Journal Title

      Proceedings of the 6th IFAC Workshop on Time-Delay Systems (CD-ROM)

    • Related Report
      2006 Annual Research Report
  • [Presentation] Synchronization of Chaotic Systems in Unidirectional Ring Networks with Delay, The 6^<th> EUROMECH Nonlinear2008

    • Author(s)
      T. Oguchi, H. Nijmeijer
    • Organizer
      The 6^<th> EUROMECH Nonlinear Dynamics Conference
    • Place of Presentation
      Accepted
    • Year and Date
      2008-06-04
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of Chaotic Systems in Unidirectional Ring Networks with Delay2008

    • Author(s)
      T.Oguchi, H.Nijmeijer
    • Organizer
      The 6th EUROMECH Nonlinear Dynamics Conference
    • Place of Presentation
      St.Petersburg,Russia
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of Four Identical Nonlinear Systems with Time-delay2008

    • Author(s)
      T.Oguchi, H.Nijmeijer, T.Yamamoto, T.Kniknie
    • Organizer
      The 17th IFAC World Congress
    • Place of Presentation
      Seoul,Korea
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of Four Identical Nonlinear Systems with Time-delay2008

    • Author(s)
      T. Oguchi, H. Nijmeijer, T. Yamamoto, T. Kniknie
    • Organizer
      The 17^<th> IFAC World Congress
    • Place of Presentation
      Accepted
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of coupled nonlinear systems with time-delay2007

    • Author(s)
      T.Yamamoto, T.Oguchi, H.Nijmeijer
    • Organizer
      European Control Conference 2007
    • Place of Presentation
      Coss,Greece
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Network synchronization with(out) time delay2007

    • Author(s)
      H.Nijmeijer, A.Pogromsky, T.Oguchi, Y.Yamamoto
    • Organizer
      International Symposium on Synchronization in Complex Networks
    • Place of Presentation
      Leuven,Belgium
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of Nonlinear systems by bidirectional coupling with Time-varying delay2007

    • Author(s)
      T.Oguchi, T.Yamamoto, H.Nijmeijer
    • Organizer
      The 7th IFAC Workshop on Time Delay Systems
    • Place of Presentation
      Nantes,France
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of networked chaotic systems with delay2007

    • Author(s)
      T.Oguchi, H.Nijmeijer, T.Yamamoto, T.Kniknie
    • Organizer
      第50回自動制御連合講演会
    • Place of Presentation
      横浜
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of coupled nonlinear systems with time-delay2007

    • Author(s)
      T. Yamamoto, T. Oguchi, H. Nijmeijer
    • Organizer
      European Control Conference 2007
    • Place of Presentation
      Coss, Greece
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Network synchronization with(out) time delay2007

    • Author(s)
      H. Nijmeijer, A. Pogromsky, T. Oguchi, Y. Yamamoto
    • Organizer
      International Symposium on Synchronization in Complex Networks
    • Place of Presentation
      Leuven, Belgium
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronisation of nonlinear systems by bidirectional coupling with time-varying delay2007

    • Author(s)
      T. Oguchi, T,. Yamamoto, H. Nijmeijer
    • Organizer
      The 7th IFAC Workshop on Time Delay Systems
    • Place of Presentation
      Nantes, France
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of networked chaotic systems with delay2007

    • Author(s)
      T. Oguchi, H. Nijmeijer, T. Yamamoto, T. Kniknie
    • Organizer
      The 50^<th> Japan Joint Conference on Automatic Control
    • Place of Presentation
      Yokohama
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronisation of Nonlinear Systems by Bidirectional Coupling with Time-varying Delay2007

    • Author(s)
      T. Oguchi, T. Yamamoto, H. Nijmeijer
    • Organizer
      the 7th IFAC Workshop on Time Delay Systems
    • Place of Presentation
      Nantes, France
    • Related Report
      2007 Annual Research Report
  • [Presentation] Anticipating Synchronization of Nonlinear Systems with Systems Uncertainties2006

    • Author(s)
      T.Oguchi, H.Nijmeijer
    • Organizer
      The 6th IFAC Workshop on Time Delay Systems
    • Place of Presentation
      L'Aquila,Italy
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of nonlinear oscillators by bidirectional diffusive coupling with time delay2006

    • Author(s)
      T.Yamamoto, T.Oguchi, H.Nijmeijer
    • Organizer
      第49回自動制御連合講演会
    • Place of Presentation
      神戸
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Anticipating Synchronization of Nonlinear Systems with Uncertainties2006

    • Author(s)
      T. Oguchi, H. Nijmeijer
    • Organizer
      The 6^<th> IFAC Workshop on Time Delay Systems
    • Place of Presentation
      L'Aquila, Italy
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Synchronization of nonlinear oscillators by bidirectional diffusive coupling with time delay2006

    • Author(s)
      T. Yamamoto, T. Oguchi, H. Nijmeijer
    • Organizer
      The 49^<th> Japan Joint Conference on Automatic Control
    • Place of Presentation
      Kobe
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary

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Published: 2006-04-01   Modified: 2016-04-21  

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