Stability Gain Design Method Based on <i>L</i>₂ Norms for Differentially Flat Systems

• FUJII Yasuhiro

  Graduate School of Science and Technology, Tokyo University of Science

• NAKAMURA Hisakazu

  Graduate School of Science and Technology, Tokyo University of Science

• SATO Yasuyuki

  Faculty of Engineering, Tokyo University of Science

Bibliographic Information

Other Title

• 微分フラットシステムに対する<i>L</i>₂規範に基づく安定化ゲイン設計法
• 微分フラットシステムに対するL₂規範に基づく安定化ゲイン設計法
• ビブン フラット システム ニ タイスル L ₂ キハン ニ モトズク アンテイカ ゲイン セッケイホウ

Abstract

We consider input-to-state-stability gain (ISS-gain) design for a differentially flat system disturbed by bounded noise. Firstly, we design a C^∞ differential strict control Lyapunov function (CLF) for the augmented linear system on the extended state space. The CLF satisfies predetermined L₂ norms performance by solving state feedback H_∞ control problems to attenuate persistent disturbance levels. Then, an Input-state-stability CLF (ISS-CLF) is derived from the CLF by applying a dynamic extension method and a minimum projection method. The ISS-CLF and the predetermined L₂ norms performance give the analytic ISS gain function. Finally, we specify the L₂ norms performance bounds of the disturbance attenuation controller for the differentially flat system. The effectiveness of the proposed method is confirmed by computer simulation of marine vessel control.

Journal

• Transactions of the Society of Instrument and Control Engineers

  Transactions of the Society of Instrument and Control Engineers 56 (5), 259-268, 2020

  The Society of Instrument and Control Engineers

Keywords

• nonlinear control
• minimum projection method
• control Lyapunov function
• input-state stability
• static feedback control

Details

• CRID: 1390848250110605184
• NII Article ID: 130007842347
• NII Book ID: AN00072392
• DOI: 10.9746/sicetr.56.259
• ISSN: 18838189
• ISSN: 04534654
• NDL BIB ID: 030455771
• Web Site: http://id.ndl.go.jp/bib/030455771
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I030455771
• Web Site: https://www.jstage.jst.go.jp/article/sicetr/56/5/56_259/_pdf
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed