Well-formed dynamics under quasi-static state feedback

J. Rudolph

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 349-360
  • ISSN: 0137-6934

Abstract

top
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.

How to cite

top

Rudolph, J.. "Well-formed dynamics under quasi-static state feedback." Banach Center Publications 32.1 (1995): 349-360. <http://eudml.org/doc/262627>.

@article{Rudolph1995,
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.},
author = {Rudolph, J.},
journal = {Banach Center Publications},
keywords = {flat; linear controllable; quasi-static state feedback},
language = {eng},
number = {1},
pages = {349-360},
title = {Well-formed dynamics under quasi-static state feedback},
url = {http://eudml.org/doc/262627},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Rudolph, J.
TI - Well-formed dynamics under quasi-static state feedback
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 349
EP - 360
AB - 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.
LA - eng
KW - flat; linear controllable; quasi-static state feedback
UR - http://eudml.org/doc/262627
ER -

References

top
  1. [1] R. Aris, Introduction to the Analysis of Chemical Reactors, Prentice-Hall, Englewood Cliffs, 1965. 
  2. [2] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969. 
  3. [3] P. Brunovský, A classification of linear controllable systems, Kybernetika 6 (1970), 173-187. Zbl0199.48202
  4. [4] B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic state feedback linearization, SIAM J. Control Optim. 29 (1991), 38-57. Zbl0739.93021
  5. [5] P. M. Cohn, Free Rings and their Relations, 2nd edition, Academic Press, London, 1985. Zbl0659.16001
  6. [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. [7] E. Delaleau et M. Fliess, Algorithme de structure, filtrations et découplage, C. R. Acad. Sci. Paris Sér. I 315 (1992), 101-106. Zbl0791.68113
  8. [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. Zbl0852.93016
  9. [9] M. Fliess, Automatique et corps différentiels, Forum Math. 1 (1989), 227-238. Zbl0701.93048
  10. [10] M. Fliess, Generalized controller canonical forms for linear and nonlinear dynamics, IEEE Trans. Automat. Control 35 (1990), 994-1001. Zbl0724.93010
  11. [11] M. Fliess, Some basic structural properties of generalized linear systems, Systems Control Lett. 15 (1990), 391-396. Zbl0727.93024
  12. [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. [13] M. Fliess, Some remarks on the Brunovský canonical form, Kybernetika 29 (1993), 417-422. Zbl0806.93007
  14. [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. Zbl0776.93038
  15. [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. [16] A. Isidori, Nonlinear Control Systems: An Introduction, Springer, New York, 1989. 
  17. [17] B. Jakubczyk, Dynamic feedback equivalence of nonlinear control systems, preprint. Zbl0712.93027
  18. [18] J. Johnson, Differential dimension polynomials and a fundamental theorem on differential modules, Amer. J. Math. 91 (1969), 239-248. Zbl0179.34303
  19. [19] J. Johnson, Kähler differentials and differential algebra, Ann. of Math. 89 (1969), 92-98. Zbl0179.34302
  20. [20] E. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973. Zbl0264.12102
  21. [21] A. Krener, Normal forms for linear and nonlinear systems, Contemp. Math. 68 (1987), 157-189. 
  22. [22] S. Lang, Algebra, Addison-Wesley, Reading, 1971. 
  23. [23] P. Martin, Contribution à l'étude des systèmes différentiellement plats, Thèse, Ecole des Mines de Paris, 1992. 
  24. [24] H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems, Springer, New York, 1990. Zbl0701.93001
  25. [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. [26] J. F. Ritt, Differential Algebra, Amer. Math. Soc., New York, 1950. 
  27. [27] P. Rouchon, Necessary condition and genericity of dynamic feedback linearization, J. Math. Systems Estim. Control 4 (1994), 1-14. Zbl0818.93012
  28. [28] J. Rudolph, Une forme canonique en bouclage quasi statique, C. R. Acad. Sci. Paris Sér. I 316 (1993), 1323-1328. 
  29. [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. Zbl0925.93107
  30. [30] J. Rudolph, Viewing input-output system equivalence from differential algebra, J. Math. Systems Estim. Control 4 (1994), 353-383. Zbl0806.93012
  31. [31] J. Rudolph, Duality in time-varying linear systems: a module theoretic approach, Linear Algebra Appl., to appear. Zbl0864.93035
  32. [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. Zbl0925.93133
  33. [33] W. Sluis, Absolute Equivalence and its Applications to Control Theory, PhD Thesis, University of Waterloo, 1992. 
  34. [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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.