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A Characterization of Normal Forms for Control Systems
- 作者:Boumediene Hamzi (1)
Jeroen S. W. Lamb (1) Debra Lewis (2)
1. Department of Mathematics ; Imperial College London ; London ; SW7 2AZ ; UK 2. Mathematics Department ; UC Santa Cruz ; Santa Cruz ; CA ; 95064 ; USA
- 关键词:Nonlinear control systems ; Inner product normal forms ; 34A34 ; 93C10 ; 93C15
- 刊名:Journal of Dynamical and Control Systems
- 出版年:2015
- 出版时间:April 2015
- 年:2015
- 卷:21
- 期:2
- 页码:273-284
- 全文大小:234 KB
- 参考文献:1. Arnold VI. Geometrical methods in the theory of ordinary differential equations. Berlin: Springer; 1983. CrossRef
2. Barbot J-P, Monaco S, Normand-Cyrot D. Quadratic forms and approximated feedback linearization in discrete time. Int J Control 1997;67(4):567鈥?87. CrossRef 3. Belitskii GR. Invariant normal forms and formal series. Funct Anal Appl. 1979;13:59鈥?0. CrossRef 4. Belitskii GR. C鈭?normal forms of local vector fields. Acta Appl Math 2002;70:23鈥?1. CrossRef 5. Chow S-N, Li C , Wang D. Normal forms and bifurcation of planar vector fields. Cambridge: Cambridge University Press; 1994. CrossRef 6. Courant R, Hilbert D. Methods of mathematical physics, vol. II. New York: Interscience; 1961. 7. Elphick C, Tirapegui E, Brachet ME, Coullet P, Iooss G. A simple global characterization for normal forms of singular vector fields. Physica D. 1987;29: 95鈥?27. CrossRef 8. Elphick C. Global aspects of hamiltonian normal forms. Phys Lett A. 1988; 127: 418鈥?24. CrossRef 9. Guckenheimer J, Holmes P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Berlin: Springer; 1983. CrossRef 10. Hamzi B, Krener AJ, Kang W. The controlled center dynamics of discrete-time control bifurcations. Syst Control Lett. 2006;55(7):585鈥?96. CrossRef 11. Hamzi B, Kang W, Krener AJ. The controlled center dynamics. SIAM J Multiscale Model Simul. 2005;3(4):838鈥?52. CrossRef 12. Hamzi B, Kang W, Barbot J-P. Analysis and control of Hopf bifurcations. SIAM J Control Optim. 2004;42(6):2200鈥?220. CrossRef 13. Hamzi B, Barbot J-P, Monaco S, Normand-Cyrot D. Nonlinear discrete-time control of systems with a Naimark-Sacker bifurcation. Syst Control Lett. 2001;44:245鈥?58. CrossRef 14. Hamzi B. Quadratic stabilization of nonlinear control systems with a double-zero control bifurcation, Proceedings of the 5th IFAC symposium on Nonlinear Control Systems (NOLCOS鈥?001) 2001: 161鈥?66. 15. Hamzi B, Barbot J-P, Kang W. Normal forms for discrete-time parameterized systems with uncontrollable linearization, Proceedings of the 38th IEEE Conference on Decision and Control 1999: 2035鈥?039. 16. Hamzi B, Tall IA. Normal forms for discrete-time control systems, Proceedings of the 42nd IEEE Conference on Decision and Control 2003;2:1357鈥?361. 17. Kang W., Krener AJ. Extended quadratic controller normal form and dynamic state feedback linearization of nonlinear systems. SIAM J. Control Optim. 1992;30:1319鈥?337. CrossRef 18. Kang W, Krener AJ. 2006. Normal forms of nonlinear control systems. In Perruquetti W, Barbot, J-P, editors. Chaos in automatic control. p. 345鈥?76. 19. Meyer KR. Normal forms for the general equilibrium. Funkcialaj Ekvacioj 1984;27:261鈥?71. 20. Meyer KR, Hall GR, Offin D. Introduction to Hamiltonian dynamical systems and the N-body problem. Berlin: Springer; 2009. 21. Murdock J. Normal forms and unfoldings for local dynamical systems. Berlin: Springer; 2003. CrossRef 22. Murdock J. Hypernormal form theory: foundations and algorithms. J Differ Equ. 2004;205:424鈥?65. CrossRef 23. Tall IA, Respondek W. Feedback classification of nonlinear single-input control systems with controllable linearization: normal forms, canonical forms, and invariants. SIAM J Control Optim. 2003;41(5):1498鈥?531. CrossRef 24. Tall IA, Respondek W. 2004. Weighted canonical forms. Proceedings of the 43rd IEEE Conference on Decision and Control, pp. 1617鈥?622. 25. Respondek W, Tall IA. 2006. Feedback equivalence of nonlinear control systems: a survey on formal approach. In W. Perruquetti and J-P. Barbot editors. Chaos in Automatic Control. p. 137鈥?62. 26. Poincar茅 H. M茅moire sur les courbes d茅finies par une 茅quation diff茅rentielle. J Maths Pures Appl. 1885;4(1):167鈥?44.
- 刊物类别:Mathematics and Statistics
- 刊物主题:Mathematics
Calculus of Variations and Optimal Control Analysis Applications of Mathematics Systems Theory and Control
- 出版者:Springer Netherlands
- ISSN:1573-8698
文摘
Our goal in this paper is to generalize the method of inner-product normal forms to nonlinear control systems.
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