Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1995 | 32 | 1 | 349-360
Tytuł artykułu

Well-formed dynamics under quasi-static state feedback

Treść / Zawartość
Warianty tytułu
Języki publikacji
Well-formed dynamics are a generalization of classical dynamics, to which they are equivalent by a quasi-static state feedback. In case such a dynamics is flat, i.e., equivalent by an endogenous feedback to a linear controllable dynamics, there exists a Brunovský type canonical form with respect to a quasi-static state feedback.
Słowa kluczowe
Opis fizyczny
  • Institut für Systemdynamik und Regelungstechnik, Universität Stuttgart, D-70550 Stuttgart, Germany
  • [1] R. Aris, Introduction to the Analysis of Chemical Reactors, Prentice-Hall, Englewood Cliffs, 1965.
  • [2] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969.
  • [3] P. Brunovský, A classification of linear controllable systems, Kybernetika 6 (1970), 173-187.
  • [4] B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic state feedback linearization, SIAM J. Control Optim. 29 (1991), 38-57.
  • [5] P. M. Cohn, Free Rings and their Relations, 2nd edition, Academic Press, London, 1985.
  • [6] E. Delaleau, Lowering orders of input derivatives in generalized state representations of nonlinear systems, in: Proc. IFAC-Symposium NOLCOS'92, Bordeaux, M. Fliess (ed.), 1992, 209-213.
  • [7] E. Delaleau et M. Fliess, Algorithme de structure, filtrations et découplage, C. R. Acad. Sci. Paris Sér. I 315 (1992), 101-106.
  • [8] E. Delaleau and W. Respondek, Lowering the orders of derivatives of controls in generalized state space systems, J. Math. Systems Estim. Control, to appear.
  • [9] M. Fliess, Automatique et corps différentiels, Forum Math. 1 (1989), 227-238.
  • [10] M. Fliess, Generalized controller canonical forms for linear and nonlinear dynamics, IEEE Trans. Automat. Control 35 (1990), 994-1001.
  • [11] M. Fliess, Some basic structural properties of generalized linear systems, Systems Control Lett. 15 (1990), 391-396.
  • [12] M. Fliess, Some remarks on a new characterization of linear controllability, in: Prepr. 2nd IFAC Workshop ``System Structure and Control'', Prague, Sept. 1992, 8-11.
  • [13] M. Fliess, Some remarks on the Brunovský canonical form, Kybernetika 29 (1993), 417-422.
  • [14] M. Fliess, J. Lévine, P. Martin et P. Rouchon, Sur les systèmes non linéaires différentiellement plats, C. R. Acad. Sci. Paris Sér. I 315 (1992), 619-624.
  • [15] S. T. Glad, Nonlinear state space and input output descriptions using differential polynomials, in: New Trends in Nonlinear Control Theory, J. Descusse, M. Fliess, A. Isidori and D. Leborgne (eds.), Lecture Notes Control Inform. Sci. 122, Springer, 1988, 182-189.
  • [16] A. Isidori, Nonlinear Control Systems: An Introduction, Springer, New York, 1989.
  • [17] B. Jakubczyk, Dynamic feedback equivalence of nonlinear control systems, preprint.
  • [18] J. Johnson, Differential dimension polynomials and a fundamental theorem on differential modules, Amer. J. Math. 91 (1969), 239-248.
  • [19] J. Johnson, Kähler differentials and differential algebra, Ann. of Math. 89 (1969), 92-98.
  • [20] E. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.
  • [21] A. Krener, Normal forms for linear and nonlinear systems, Contemp. Math. 68 (1987), 157-189.
  • [22] S. Lang, Algebra, Addison-Wesley, Reading, 1971.
  • [23] P. Martin, Contribution à l'étude des systèmes différentiellement plats, Thèse, Ecole des Mines de Paris, 1992.
  • [24] H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems, Springer, New York, 1990.
  • [25] J. B. Pomet, C. H. Moog, and A. Aranda, A non-exact Brunovský form and dynamic feedback linearization, in: Proc. 31st CDC IEEE, Tucson, 1992, 2012-2017.
  • [26] J. F. Ritt, Differential Algebra, Amer. Math. Soc., New York, 1950.
  • [27] P. Rouchon, Necessary condition and genericity of dynamic feedback linearization, J. Math. Systems Estim. Control 4 (1994), 1-14.
  • [28] J. Rudolph, Une forme canonique en bouclage quasi statique, C. R. Acad. Sci. Paris Sér. I 316 (1993), 1323-1328.
  • [29] J. Rudolph, A canonical form under quasi-static feedback, in: Systems and Networks: Mathematical Theory and Applications, U. Helmke, R. Mennicken, and J. Saurer (eds.), 1993, 445-448.
  • [30] J. Rudolph, Viewing input-output system equivalence from differential algebra, J. Math. Systems Estim. Control 4 (1994), 353-383.
  • [31] J. Rudolph, Duality in time-varying linear systems: a module theoretic approach, Linear Algebra Appl., to appear.
  • [32] J. Rudolph and S. El Asmi, Filtrations and Hilbert polynomials in control theory, in: Systems and Networks: Mathematical Theory and Applications, U. Helmke, R. Mennicken, and J. Saurer (eds.), 1994, 449-452.
  • [33] W. Sluis, Absolute Equivalence and its Applications to Control Theory, PhD Thesis, University of Waterloo, 1992.
  • [34] M. Zeitz, Canonical forms for nonlinear systems, in: Nonlinear Control Systems Design, Selected Papers from the IFAC-Symposium, Capri/Italy 1989, A. Isidori (ed.), Pergamon Press, Oxford, 1990, 33-38.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.