Development of Parametric Controller to Enhance Resilience of Dynamical Systems

• Project/Area Number: 16K00332
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Soft computing
• Research Institution: Kagawa University
• Principal Investigator: Fujimoto Ken'ichi 香川大学, 創造工学部, 准教授 (20300626)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 複雑系 / レジリエンス性 / パラメータ制御系 / リアプノフ指数 / スペクトル半径 / 分岐回避 / 動的システム / 安定解 / 離散時間動的システム / 非周期点 / 安定固定点 / レジリエンス / 最大リアプノフ指数 / 非自律系 / ストロボ写像 / 数理工学

Outline of Final Research Achievements

The purpose of this study is to develop parametric control systems for handling the state stability of complex systems described by nonlinear differential or difference equations. In dynamical systems, steady-state stability depends on the value of system parameters. Changing the parameter value can lead to bifurcation that means the disappearance of the current state and the occurrence of another state. The principal investigator has developed parametric controllers to handle the steady-state stability defined with the Lyapunov exponents or the spectral radius of a linearization system. The parametric controllers are available to avoid bifurcations caused by unexpected changes in system-parameter values.

Academic Significance and Societal Importance of the Research Achievements

本研究では，常微分方程式や常差分方程式で記述される数理モデルにみられる安定な状態が，システムパラメータ変化によって急変することを回避するパラメータ制御系を開発した。開発した制御系は数理モデルとして記述できるさまざま複雑系に対して適用可能であり，生命系，電力網，情報通信ネットワークなどの幅広い分野におけるシステムについて，そのレジリエンス性を向上させるための基礎技術となりうる。

Research Products

• [Journal Article] Control Technique of Maximum Local Lyapunov Exponent on Stable Periodic Solution in Continuous-Time Non-Autonomous Dynamical Systems (2016)
  • Author(s): K. Fujimoto, T. Otsu, H. Kitajima, and T. Ueta
  • Journal Title: International Journal of Computing, Communication and Instrumentation Engineering Volume: 3 Issue: 2 Pages: 349-353
  • DOI: 10.15242/ijccie.ae0616114
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] A Method to Compute Gradient of Local Lyapunov Exponents (2020)
  • Author(s): Ken'ichi Fujimoto
  • Organizer: 28th Bucharest International Conference on Latest Trends in Engineering and Technology
  • Int'l Joint Research
• [Presentation] A Method to Control Stability Index of Quasi-Periodic Behavior (2018)
  • Author(s): Ken’ichi Fujimoto
  • Organizer: The 8th International Conference on Electronics, Communications and Networks (CECNet 2018)
  • Int'l Joint Research
• [Presentation] Controller to Avoid Bifurcations of Stable Fixed Point Using Spectral Radius Optimization (2017)
  • Author(s): K. Fujimoto
  • Organizer: 6th International Conference on Advances in Engineering and Technology
  • Int'l Joint Research
• [Presentation] スペクトル半径最適化法を用いた安定固定点の分岐回避制御系 (2017)
  • Author(s): 藤本 憲市
  • Organizer: 平成29年電気学会電子・情報・システム部門大会
• [Presentation] Bifurcation Avoidance of Stable Periodic Motion in Non-Autonomous Dynamical System (2016)
  • Author(s): K. Fujimoto
  • Organizer: International Conference Proceedings of Eminent Association of Pioneers
  • Place of Presentation: Kuala Lumpur, Malaysia
  • Year and Date: 2016-08-22
  • Int'l Joint Research
• [Presentation] Control Technique of Maximum Local Lyapunov Exponent on Stable Periodic Solution in Continuous-Time Non-Autonomous Dynamical Systems (2016)
  • Author(s): K. Fujimoto, T. Otsu, H. Kitajima, and T. Ueta
  • Organizer: International Conference on Advances in Engineering and Technology Research (AETR-16)
  • Place of Presentation: Bangkok, Thailand
  • Year and Date: 2016-06-23
  • Int'l Joint Research