Download PDF - Infinitesimal Brunovský form for nonlinear systems with applications to Dynamic LinearizationAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Infinitesimal Brunovský form for nonlinear systems with applications to Dynamic Linearization

Authors 1, 2, 3

Affiliations

  1. Secc. de Control Automático, Dep. de Ingen. Elétrica, CINVESTAV - IPN, Ap. Postal 14-740, 07000 México, D.F., Mexico
  2. Laboratoire d'Automatique de Nantes, U.R.A. C.N.R.S. 823, E. C. N., 1 Rue de la Noë, 44072 Nantes Cédex, France
  3. I.N.R.I.A., 2004 Route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cédex, France

Abstract

We define, in an infinite-dimensional differential geometric framework, the 'infinitesimal Brunovský form' which we previously introduced in another framework and link it with equivalence via diffeomorphism to a linear system, which is the same as linearizability by 'endogenous dynamic feedback'.

Keywords

ENG
flat systems, dynamic feedback linearization, Brunovský canonical form, nonlinear control systems, endogenous dynamic feedback, Pfaffian systems, linearized control system

Bibliography

  1. E. Aranda, C. H. Moog and J.-B. Pomet, A linear algebraic framework for dynamic feedback linearization, IEEE Trans. Automatic Control, 40 (1995), 127-132.
  2. E. Aranda, C. H. Moog and J.-B. Pomet, Feedback linearization: a linear algebraic approach, in: 22nd IEEE Conf. on Dec. and Cont., Dec. 1993.
  3. P. Brunovský, A classification of linear controllable systems, Kybernetika 6 (1970), 176-188.
  4. B. Charlet, J. Lévine and R. Marino, On dynamic feedback linearization, Syst. & Contr. Lett. 13 (1989), 143-151.
  5. B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic feedback linearization, SIAM J. Contr. Opt. 29 (1991), 38-57.
  6. J.-M. Coron, Linearized control systems and applications to smooth stabilization, SIAM J. Contr. Opt. 32 (1994), 358-386.
  7. M. D. Di Benedetto, J. Grizzle and C. H. Moog, Rank invariants of nonlinear systems, SIAM J. Contr. Opt. 27 (1989), 658-672.
  8. M. Fliess, Automatique et corps différentiels, Forum Math. 1 (1989), 227-238.
  9. M. Fliess, Some remarks on the Brunovský canonical form, preprint, L.S.S., Ec. Sup. d'Elec., Gif-sur-Yvette, France, 1992, to appear in Kybernetika.
  10. M. Fliess and S. T. Glad, An algebraic approach to linear and nonlinear control, in: H. L. Trentelman and J. C. Willems (eds.), Essays on Control: Perspectives in the Theory and its Applications, PSCT 14, Birkhäuser, Boston, 1993.
  11. M. Fliess, J. Lévine, P. Martin and P. Rouchon, On differentially flat nonlinear systems, in: 2nd. IFAC NOLCOS Symposium, 1992, 408-412.
  12. M. Fliess, J. Lévine, P. Martin and P. Rouchon, Sur les systèmes non linéaires différentiellement plats, C. R. Acad. Sc. Paris, 315-I (1992), 619-624.
  13. A. Ilchmann, I. Nürnberger and W. Schmale, Time-varying polynomial matrix systems, Int. J. Control 40 (1984), 329-362.
  14. B. Jakubczyk, Remarks on equivalence and linearization of nonlinear systems, in: 2nd. IFAC NOLCOS Symposium, 1992, 393-397.
  15. B. Jakubczyk, Dynamic feedback equivalence of nonlinear control systems, preprint, 1993.
  16. P. Martin, Contribution à l'étude des systèmes non linéaires différentiellement plats, Thèse de Doctorat, Ecole des Mines de Paris, 1992.
  17. P. Martin, A geometric sufficient conditions for flatness of systems with m inputs and m+1 states, in: 22nd IEEE Conf. on Dec. and Cont., Dec. 1993, 3431-3435.
  18. P. Martin, A criterion for flatness with structure {1,...,1,2}, preprint, 1992.
  19. P. Martin and P. Rouchon, Systems without drift and flatness, in: Int. Symp. on Math. Theory on Networks and Syst., Regensburg, August 1993.
  20. J.-B. Pomet, On dynamic feedback linearization of four-dimensional affine control systems with two inputs, preprint, 1993, INRIA report No 2314.
  21. J.-B. Pomet, A differential geometric setting for dynamic equivalence and dynamic linearization, this volume, 319-339.
  22. J.-B. Pomet, C. H. Moog and E. Aranda, A non-exact Brunovský form and dynamic feedback linearization, in: Proc. 31st. IEEE Conf. Dec. Cont., 1992, 2012-2017.
  23. E. D. Sontag, Finite-dimensional open-loop control generators for nonlinear systems, Int. J. Control 47 (1988), 537-556.
  24. H. J. Sussmann and V. Jurdjevic, Controllability of nonlinear systems, J. Diff. Eq. 12 (1972), 95-116.
  25. W. A. Wolovich, Linear Multivariable Systems, Applied Math. Sci. 11, Springer, 1974.
Banach Center Publications
1995/32/1
Export to PBN, Opens in new tab
Pages:
19-33
Main language of publication
English
Published
1995
Exact and natural sciences