Download PDF - Well-formed dynamics under quasi-static state feedbackAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Well-formed dynamics under quasi-static state feedback

Authors 1

Affiliations

  1. Institut für Systemdynamik und Regelungstechnik, Universität Stuttgart, D-70550 Stuttgart, Germany

Abstract

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.

Bibliography

  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.
Banach Center Publications
1995/32/1
Export to PBN, Opens in new tab
Pages:
349-360
Main language of publication
English
Published
1995
Exact and natural sciences