PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1995 | 32 | 1 | 319-339
Tytuł artykułu

A differential geometric setting for dynamic equivalence and dynamic linearization

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents an (infinite-dimensional) geometric framework for control systems, based on infinite jet bundles, where a system is represented by a single vector field and dynamic equivalence (to be precise: equivalence by endogenous dynamic feedback) is conjugation by diffeomorphisms. These diffeomorphisms are very much related to Lie-Bäcklund transformations. It is proved in this framework that dynamic equivalence of single-input systems is the same as static equivalence.
Rocznik
Tom
32
Numer
1
Strony
319-339
Opis fizyczny
Daty
wydano
1995
Twórcy
  • I.N.R.I.A., 2004 Route des Lucioles, B.P. 93, 06902 Sophia Antipolis, France
Bibliografia
  • [1] R. L. Anderson and N. H. Ibragimov, Lie-Bäcklund Transformations in Applications, SIAM Stud. Appl. Math., SIAM, Philadelphia, 1979.
  • [2] E. Aranda-Bricaire, C. H. Moog and J.-B. Pomet, A linear algebraic framework for dynamic feedback linearization, IEEE Trans. Automat. Control 40 (1995), 127-132.
  • [3] E. Aranda-Bricaire, C. H. Moog and J.-B. Pomet, Infinitesimal Brunovský form for nonlinear systems with applications to dynamic linearization, this volume.
  • [4] N. Bourbaki, Eléments de Mathématique, Espaces Vectoriels Topologiques, chap. 1, Masson, Paris, 1981.
  • [5] P. Brunovský, A classification of linear controllable systems, Kybernetika 6 (1970), 176-188.
  • [6] B. Charlet, J. Lévine and R. Marino, On dynamic feedback linearization, Systems Control Lett. 13 (1989), 143-151.
  • [7] B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic feedback linearization, SIAM J. Control Optim. 29 (1991), 38-57.
  • [8] G. Conte, A.-M. Perdon and C. Moog, The differential field associated to a general analytic nonlinear system, IEEE Trans. Automat. Control 38 (1993), 1120-1124.
  • [9] E. Delaleau, Sur les dérivées de l'entrée en représentation et commande des systèmes non-linéaires, Thèse de l'Unviversité Paris XI, Orsay, 1993.
  • [10] M. Fliess, Automatique et corps différentiels, Forum Math. 1 (1989), 227-238.
  • [11] M. Fliess, Décomposition en cascade des systèmes automatiques et feuilletages invariants, Bull. Soc. Math. France 113 (1985), 285-293.
  • [12] M. Fliess, J. Lévine, P. Martin and P. Rouchon, On differentially flat nonlinear systems, in: 2nd IFAC NOLCOS Symposium, 1992, 408-412.
  • [13] M. Fliess, J. Lévine, P. Martin and P. Rouchon, Sur les systèmes non linéaires différentiellement plats, C. R. Acad. Sci. Paris Sér. I 315 (1992), 619-624.
  • [14] M. Fliess, J. Lévine, P. Martin and P. Rouchon, Linéarisation par bouclage dynamique et transformations de Lie-Bäcklund, ibid., to appear.
  • [15] M. Fliess, J. Lévine, P. Martin and P. Rouchon, Towards a new differential geometric setting in nonlinear control, Presented at International Geometrical Colloquium, Moscow, May 1993, and to appear in the proceedings.
  • [16] E. Goursat, Le problème de Bäcklund, Mém. Sci. Math. 6, Gauthier-Villars, Paris, 1925.
  • [17] R. S. Hamilton, The Inverse Function Theorem of Nash and Moser, Bull. Amer. Math. Soc. 7 (1982), 65-222.
  • [18] B. Jakubczyk, Remarks on equivalence and linearization of nonlinear systems, in: 2nd IFAC NOLCOS Symposium, 1992, 393-397.
  • [19] B. Jakubczyk, Dynamic feedback equivalence of nonlinear control systems, preprint, 1993.
  • [20] I. S. Krasil'shchik, V. V. Lychagin and A. M. Vinogradov, Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Adv. Stud. Contemp. Math. 1, Gordon & Breach, 1986.
  • [21] P. Martin, Contribution à l'étude des systèmes non linéaires différentiellement plats, Thèse de Doctorat, Ecole des Mines de Paris, 1992.
  • [22] P. Otterson and G. Svetlichny, On derivative-dependent deformations of differential maps, J. Differential Equations 36 (1980), 270-294.
  • [23] F. A. E. Pirani, D. C. Robinson and W. F. Shadwick, Local jet bundle formulation of Bäcklund transformations, Math. Phys. Stud., Reidel, Dordrecht, 1979.
  • [24] 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.
  • [25] J.-F. Pommaret, Géométrie différentielle algébrique et théorie du contrôle, C. R. Acad. Sci. Paris Sér. I 302 (1986), 547-550.
  • [26] D. J. Saunders, The Geometry of Jet Bundles, London Math. Soc. Lecture Note Ser. 142, Cambridge University Press, Cambridge, 1989.
  • [27] W. F. Shadwick, Absolute equivalence and dynamic feedback linearization, Systems Control Lett. 15 (1990), 35-39.
  • [28] A. M. Vinogradov, Local symmetries and conservation laws, Acta Appl. Math. 2 (1984), 21-78.
  • [29] J. C. Willems, Paradigms and puzzles in the theory of dynamical systems, IEEE Trans. Automat. Control 36 (1991), 259-294.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv32z1p319bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.