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Analytic normal forms and symmetries of strict feedforward control systems
Author(s) -
Tall Issa Amadou,
Respondek Witold
Publication year - 2010
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1505
Subject(s) - homogeneous space , diffeomorphism , scaling , constructive , symmetry (geometry) , feed forward , mathematics , translation (biology) , pure mathematics , control theory (sociology) , control (management) , computer science , artificial intelligence , geometry , biochemistry , chemistry , process (computing) , control engineering , messenger rna , engineering , gene , operating system
This paper deals with the problem of convergence of normal forms of control systems. We identify an n ‐dimensional subclass of control systems, called special strict feedforward form , shortly (SSFF), possessing a normal form which is a smooth (resp. analytic) counterpart of the formal normal form of Kang. We provide a constructive algorithm and illustrate by several examples including the Kapitsa pendulum and the cart–pole system. The second part of the paper is concerned about symmetries of single‐input control systems. We show that any symmetry of a smooth system in SSFF is conjugated to a scaling translation and any 1‐parameter family of symmetries is conjugated to a family of scaling translations along the first variable. We compute explicitly those symmetries by finding the conjugating diffeomorphism. We illustrate our results by computing the symmetries of the cart–pole system. Copyright © 2009 John Wiley & Sons, Ltd.