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

2019 Fiscal Year Final Research Report

• 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
• Keywords: 制御理論 / 非線形システム / ダイナミクス / 安定論

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.

Free Research Field

システム制御理論

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。