A Characterization of Normal Forms for Control Systems

Our goal in this paper is to generalize the method of inner-product normal forms to nonlinear control systems.

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Published in:	Journal of dynamical and control systems Vol. 21; no. 2; pp. 273 - 284
Main Authors:	Hamzi, Boumediene, Lamb, Jeroen S. W., Lewis, Debra
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01-04-2015
Subjects:	Calculus of Variations and Optimal Control; Optimization Control Dynamical Systems Dynamical Systems and Ergodic Theory Mathematics Mathematics and Statistics Systems Theory Vibration Nonlinear control systems 93C10 34A34 93C15 Inner product normal forms
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Abstract	Our goal in this paper is to generalize the method of inner-product normal forms to nonlinear control systems.
AbstractList	Our goal in this paper is to generalize the method of inner-product normal forms to nonlinear control systems.
Author	Hamzi, Boumediene Lewis, Debra Lamb, Jeroen S. W.
Author_xml	– sequence: 1 givenname: Boumediene surname: Hamzi fullname: Hamzi, Boumediene email: b.hamzi@imperial.ac.uk organization: Department of Mathematics, Imperial College London – sequence: 2 givenname: Jeroen S. W. surname: Lamb fullname: Lamb, Jeroen S. W. organization: Department of Mathematics, Imperial College London – sequence: 3 givenname: Debra surname: Lewis fullname: Lewis, Debra organization: Mathematics Department, UC Santa Cruz
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Keywords	Nonlinear control systems 93C10 34A34 93C15 Inner product normal forms
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References_xml	– volume: 67 start-page: 567 issue: 4 year: 1997 ident: 9264_CR2 publication-title: Int J Control doi: 10.1080/002071797224081 contributor: fullname: J-P Barbot – volume: 4 start-page: 167 issue: 1 year: 1885 ident: 9264_CR26 publication-title: J Maths Pures Appl contributor: fullname: H Poincaré – ident: 9264_CR24 – volume-title: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields year: 1983 ident: 9264_CR9 doi: 10.1007/978-1-4612-1140-2 contributor: fullname: J Guckenheimer – volume-title: Normal forms and unfoldings for local dynamical systems year: 2003 ident: 9264_CR21 doi: 10.1007/b97515 contributor: fullname: J Murdock – volume: 127 start-page: 418 year: 1988 ident: 9264_CR8 publication-title: Phys Lett A doi: 10.1016/0375-9601(88)90207-1 contributor: fullname: C Elphick – volume: 41 start-page: 1498 issue: 5 year: 2003 ident: 9264_CR23 publication-title: SIAM J Control Optim doi: 10.1137/S0363012900381753 contributor: fullname: IA Tall – ident: 9264_CR16 – volume: 42 start-page: 2200 issue: 6 year: 2004 ident: 9264_CR12 publication-title: SIAM J Control Optim doi: 10.1137/S0363012900372714 contributor: fullname: B Hamzi – ident: 9264_CR18 – volume: 205 start-page: 424 year: 2004 ident: 9264_CR22 publication-title: J Differ Equ doi: 10.1016/j.jde.2004.02.015 contributor: fullname: J Murdock – volume: 44 start-page: 245 year: 2001 ident: 9264_CR13 publication-title: Syst Control Lett doi: 10.1016/S0167-6911(01)00136-0 contributor: fullname: B Hamzi – ident: 9264_CR25 doi: 10.1201/9781315220925-4 – volume: 70 start-page: 23 year: 2002 ident: 9264_CR4 publication-title: Acta Appl Math doi: 10.1023/A:1013909812387 contributor: fullname: GR Belitskii – volume: 30 start-page: 1319 year: 1992 ident: 9264_CR17 publication-title: SIAM J. Control Optim doi: 10.1137/0330070 contributor: fullname: W Kang – volume: 55 start-page: 585 issue: 7 year: 2006 ident: 9264_CR10 publication-title: Syst Control Lett doi: 10.1016/j.sysconle.2006.01.001 contributor: fullname: B Hamzi – volume: 27 start-page: 261 year: 1984 ident: 9264_CR19 publication-title: Funkcialaj Ekvacioj contributor: fullname: KR Meyer – volume: 3 start-page: 838 issue: 4 year: 2005 ident: 9264_CR11 publication-title: SIAM J Multiscale Model Simul doi: 10.1137/040603139 contributor: fullname: B Hamzi – volume-title: Methods of mathematical physics, vol. II year: 1961 ident: 9264_CR6 contributor: fullname: R Courant – ident: 9264_CR15 – volume-title: Normal forms and bifurcation of planar vector fields year: 1994 ident: 9264_CR5 doi: 10.1017/CBO9780511665639 contributor: fullname: S-N Chow – volume: 13 start-page: 59 year: 1979 ident: 9264_CR3 publication-title: Funct Anal Appl doi: 10.1007/BF01076439 contributor: fullname: GR Belitskii – volume: 29 start-page: 95 year: 1987 ident: 9264_CR7 publication-title: Physica D doi: 10.1016/0167-2789(87)90049-2 contributor: fullname: C Elphick – volume-title: Introduction to Hamiltonian dynamical systems and the N-body problem year: 2009 ident: 9264_CR20 doi: 10.1007/978-0-387-09724-4 contributor: fullname: KR Meyer – ident: 9264_CR14 doi: 10.1016/S1474-6670(17)35167-4 – volume-title: Geometrical methods in the theory of ordinary differential equations year: 1983 ident: 9264_CR1 doi: 10.1007/978-1-4684-0147-9 contributor: fullname: VI Arnold
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SubjectTerms	Calculus of Variations and Optimal Control; Optimization Control Dynamical Systems Dynamical Systems and Ergodic Theory Mathematics Mathematics and Statistics Systems Theory Vibration
Title	A Characterization of Normal Forms for Control Systems
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