Design methodology for mutually complementary dynamics of multidimensional nonlinear systems based on monotone preserving transformation

• Project/Area Number: 17K06499
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Control engineering/System engineering
• Research Institution: Kyushu Institute of Technology
• Principal Investigator: Ito Hiroshi 九州工業大学, 大学院情報工学研究院, 教授 (70274561)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 制御理論 / 非線形システム / ダイナミクス / 安定論 / 制御工学

Outline of Final Research Achievements

In this project, a methodology to design dynamics with performance guarantees has been developed via balancing nonlinearities of a large number of components. The notion of integral input-to-state stability is extended to recast multi-dimensional systems as equations with useful monotonicity. Then monotonicity preserving transformation has been formulated. Undesirable behavior arising from adding and connecting components is predicted and prevented by combining notions of boundedness with and without inputs. The monotonicity preserving transformation has enabled unified construction of Lyapunov functions for dynamics design. This research has reached a geometric formulation which is completely unique and has formed a breakthrough to accomplish the planned goal and beyond. Scalable design methods and an observer-based output feedback design method in the presence of measurement noise have been given global guarantees which had not been achieved in the research field.

Academic Significance and Societal Importance of the Research Achievements

様々な機能と性質をもつ物事を組み合わせ、安全で期待通りの性能の統合システムを設計する数理手法を開発した。物事には空間と時間のスケール、物理単位があり、それらが異なる物事同士をIoT社会は気軽に接続する。接続は、個別では隠れていた破壊的な振る舞いや悪循環など、元の構成物事の組み合わせでは想像できない現象を発現させる。その対処には個別状態から潜在的な悪を除去する方法もあるが、自由な接続時代（ビックデータ）では意味をなさない。そこで、本研究は物事の長所と短所を釣り合わせた結び付けを追究し、ダイナミクスの単調表現とその保存変換という新着想で数学手法を開発した。適用範囲は人工、生命、環境、社会と幅広い。

Research Products

• [Int'l Joint Research] The University of Newcastle(オーストラリア)
• [Int'l Joint Research] CNAM(フランス)
• [Int'l Joint Research] ニューカッスル大学(オーストラリア)
• [Int'l Joint Research] ソウル大学(韓国)
• [Int'l Joint Research] ニューカッスル大学(オーストラリア)
• [Journal Article] A complete characterization of integral input-to-state stability and its small-gain theorem for stochastic systems (2020)
  • Author(s): Hiroshi Ito
  • Journal Title: IEEE Trans. Automatic Control Volume: 65 Issue: 7 Pages: 3039-3052
  • DOI: 10.1109/tac.2019.2946203
  • Peer Reviewed
• [Journal Article] Interval observer of minimal error dynamics (2020)
  • Author(s): Hiroshi Ito
  • Journal Title: Automatica Volume: 113 Pages: 108794-108794
  • DOI: 10.1016/j.automatica.2019.108794
  • Peer Reviewed
• [Journal Article] A geometrical formulation to unify construction of Lyapunov functions for interconnected iISS system (2019)
  • Author(s): Hiroshi Ito
  • Journal Title: Annual Reviews in Control Volume: 48 Pages: 195-208
  • DOI: 10.1016/j.arcontrol.2019.05.004
  • Peer Reviewed
• [Journal Article] An intuitive modification of max-separable Lyapunov functions to cover non-ISS systems (2019)
  • Author(s): Hiroshi Ito
  • Journal Title: Automatica Volume: 107 Pages: 518-525
  • DOI: 10.1016/j.automatica.2019.06.020
  • Peer Reviewed
• [Journal Article] A small-gain theorem in the absence of strong iISS (2019)
  • Author(s): Hiroshi Ito, Christopher M. Kellett
  • Journal Title: IEEE Trans. Automatic Control Volume: 64 Issue: 9 Pages: 3897-3904
  • DOI: 10.1109/tac.2018.2886955
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Smaller and negative exponents in Lyapunov functions for interconnected iISS systems (2020)
  • Author(s): Hiroshi Ito
  • Organizer: The 21st IFAC World Congress
  • Int'l Joint Research
• [Presentation] Asymptotic and tracking guarantees in interval observer design for systems with unmeasured polytopic nonlinearitiess (2020)
  • Author(s): Hiroshi Ito, Thach Ngoc Dinh
  • Organizer: The 21st IFAC World Congress
  • Int'l Joint Research / Invited
• [Presentation] A fusion of max- and sum-separable Lyapunov functions capable of addressing iISS in networks (2019)
  • Author(s): Hiroshi Ito
  • Organizer: The 58th IEEE Conf. Decision Control
  • Int'l Joint Research / Invited
• [Presentation] A study on distance-based control of mobile agents for formation avoiding entire and partial reflection (2019)
  • Author(s): Hiroshi Ito, Yuichi Miyagi
  • Organizer: The 19th International Conference on Control, Automation and Systems
  • Int'l Joint Research
• [Presentation] An approach to interval observers for Takagi-Sugeno systems with attractiveness guarantees (2019)
  • Author(s): Hiroshi Ito, Thach Ngoc Dinh
  • Organizer: SICE Annual Conference 2019
  • Int'l Joint Research
• [Presentation] A closed form expression of nonlinear scalings for Lyapunov functions of ISS networks (2019)
  • Author(s): Hiroshi Ito
  • Organizer: The 11th IFAC Symposium on Nonlinear Control Systems
  • Int'l Joint Research
• [Presentation] Chamfering max-separable Lyapunov functions to accept Non-ISS in interconnected systems (2019)
  • Author(s): Hiroshi Ito
  • Organizer: 2019 American Control Conference
  • Int'l Joint Research
• [Presentation] 面取りによるiISSとISS結合システムのリアプノフ関数の統合について (2019)
  • Author(s): 伊藤 博
  • Organizer: 第6回計測自動制御学会制御部門マルチシンポジウム
• [Presentation] Adaptable iISS small-gain formulation and its application to observer-based output feedback design (2018)
  • Author(s): Hiroshi Ito, Hyungbo Shim
  • Organizer: The 57th IEEE Conf. Decision Control
  • Int'l Joint Research
• [Presentation] A smooth construction of ISS Lyapunov functions for interconnected systems (2018)
  • Author(s): Hiroshi Ito
  • Organizer: The 57th IEEE Conf. Decision Control
  • Int'l Joint Research
• [Presentation] Bypassing disturbance separability in verifying integral input-to-state stability of cascade systems (2018)
  • Author(s): Hiroshi Ito
  • Organizer: SICE Annual Conference 2018
  • Int'l Joint Research
• [Presentation] Integral input-to-state stability of cascaded systems and observer-based feedback design (2018)
  • Author(s): Hiroshi Ito
  • Organizer: 2018 American Control Conference
  • Int'l Joint Research / Invited
• [Presentation] An implicit function approach to Lyapunov functions for interconnections containing non-ISS components (2018)
  • Author(s): Hiroshi Ito
  • Organizer: The 2nd IFAC Conf. Modelling, Identification and Control of Nonlinear Systems
  • Int'l Joint Research
• [Presentation] 陰関数を使った結合iISSシステムのリアプノフ関数の新構成法について (2018)
  • Author(s): 伊藤 博
  • Organizer: 第61回自動制御連合講演会
• [Presentation] 結合システムのリアプノフ関数構成は最大分離型に傾斜を付ければiISSを包含 (2018)
  • Author(s): 伊藤 博
  • Organizer: 第5回計測自動制御学会制御部門マルチシンポジウム
• [Presentation] 大域的非線形ゲインを持つシステムの結合は角の丸い角鉢がリアプノフ関数 (2018)
  • Author(s): 伊藤 博
  • Organizer: 第5回計測自動制御学会制御部門マルチシンポジウム
• [Presentation] 結合システムのリアプノフ関数構成は最大分離型に傾斜を付ければiISSを包含 (2018)
  • Author(s): 伊藤博
  • Organizer: 第5回計測自動制御学会制御部門マルチシンポジウム
• [Presentation] 大域的非線形ゲインを持つシステムの結合は角の丸い角鉢がリアプノフ関数 (2018)
  • Author(s): 伊藤博
  • Organizer: 第5回計測自動制御学会制御部門マルチシンポジウム
• [Presentation] A new formulation of small-gain theorem without imposing strong iISS with respect to disturbances on components (2017)
  • Author(s): Hiroshi Ito, Christopher M. Kellett
  • Organizer: The 56th IEEE Conf. Decision Control
  • Int'l Joint Research
• [Presentation] Relaxing growth rate assumption for integral input-to-state stability of cascade systems (2017)
  • Author(s): Hiroshi Ito
  • Organizer: SICE Annual Conference 2017
  • Int'l Joint Research
• [Book] Positive Systems: Theory and Applications (POSTA 2018) (2019)
  • Author(s): James Lam, Yun Chen, Xingwen Liu, Xudong Zhao, Junfeng Zhang, Maria E. Valcher, Hiroshi Ito, Bjoern S. Rueffer, Li-Juan Liu, Xi-Ming Sun, Yue Wang, Hongwei Wang, Jie Lian, Jinjin Liu, Shanen Yu, Zhiqiang Li, Ting Zhang, Shuai Li, Duyu Liu et al.
  • Publisher: Springer
  • ISBN: 9783030043261
• [Remarks] JSPS科研費17K06499に関わる成果報告
  • URL: http://palm.ces.kyutech.ac.jp/~hiroshi/fsprojects/kakenmono17.html