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Adaptive stabilization of Kirchhoff's non‐linear strings by boundary displacement feedback
Author(s) -
Kobayashi Toshihiro,
Sakamoto Tetsuzo
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.839
Subject(s) - mathematics , control theory (sociology) , boundary (topology) , displacement (psychology) , string (physics) , mathematical analysis , adaptive control , linear system , nonlinear system , control (management) , physics , computer science , psychology , quantum mechanics , artificial intelligence , mathematical physics , psychotherapist
Abstract This paper is concerned with adaptive global stabilization of an undamped non‐linear string in the case where any velocity feedback is not available. The linearized system may have an infinite number of poles and zeros on the imaginary axis. In the case where any velocity feedback is not available, a parallel compensator is effective. The adaptive stabilizer is constructed for the augmented system which consists of the controlled system and a parallel compensator. It is proved that the string can be stabilized by adaptive boundary control. Copyright © 2007 John Wiley & Sons, Ltd.