On nonlinear equivalence and backstepping observer

J. de Leon; I. Souleiman; Alain Glumineau; G. Schreier

Kybernetika (2001)

  • Volume: 37, Issue: 5, page [521]-546
  • ISSN: 0023-5954

Abstract

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An observer design based on backstepping approach for a class of state affine systems is proposed. This class of nonlinear systems is determined via a constructive algorithm applied to a general nonlinear Multi Input–Multi Output systems. Some examples are given in order to illustrate the proposed methodology.

How to cite

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Leon, J. de, et al. "On nonlinear equivalence and backstepping observer." Kybernetika 37.5 (2001): [521]-546. <http://eudml.org/doc/33549>.

@article{Leon2001,
abstract = {An observer design based on backstepping approach for a class of state affine systems is proposed. This class of nonlinear systems is determined via a constructive algorithm applied to a general nonlinear Multi Input–Multi Output systems. Some examples are given in order to illustrate the proposed methodology.},
author = {Leon, J. de, Souleiman, I., Glumineau, Alain, Schreier, G.},
journal = {Kybernetika},
keywords = {design; nonlinear system; multi-input–multi-output system; backstepping approach; state affine systems; nonlinear equivalence; design; nonlinear system; multi-input–multi-output system; backstepping approach; state affine systems; nonlinear equivalence},
language = {eng},
number = {5},
pages = {[521]-546},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On nonlinear equivalence and backstepping observer},
url = {http://eudml.org/doc/33549},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Leon, J. de
AU - Souleiman, I.
AU - Glumineau, Alain
AU - Schreier, G.
TI - On nonlinear equivalence and backstepping observer
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 5
SP - [521]
EP - 546
AB - An observer design based on backstepping approach for a class of state affine systems is proposed. This class of nonlinear systems is determined via a constructive algorithm applied to a general nonlinear Multi Input–Multi Output systems. Some examples are given in order to illustrate the proposed methodology.
LA - eng
KW - design; nonlinear system; multi-input–multi-output system; backstepping approach; state affine systems; nonlinear equivalence; design; nonlinear system; multi-input–multi-output system; backstepping approach; state affine systems; nonlinear equivalence
UR - http://eudml.org/doc/33549
ER -

References

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  1. Besançon G., Bornard, G., Hammouri H., 10.1016/S0947-3580(96)70043-2, European J. Control (1996), 176–192 (1996) DOI10.1016/S0947-3580(96)70043-2
  2. Busawon K., Farza, M., Hammouri H., Observers’ synthesis for a class of nonlinear systems with application to state and parameter estimation in bioreactors, In: Proc. 36th IEEE Conference on Decision and Control, San Diego, California 1997 
  3. Busawon K., Saif M., 10.1016/S0893-9659(98)00111-6, Appl. Math. Lett. 11 (1998), 6, 109–113 (1998) MR1647133DOI10.1016/S0893-9659(98)00111-6
  4. Conte G., Moog C. H., Perdon A. M., Nonlinear Control Systems – An algebraic setting, Springer–Verlag, Berlin 1999 Zbl0920.93002MR1687965
  5. Diop S., 10.1007/BF02551378, Math. Control Signals Systems 4 (1991), 17–32 (1991) Zbl0727.93025MR1082853DOI10.1007/BF02551378
  6. Diop S., Fliess M., On nonlinear observability, In: Proc. European Control Conference (ECC’91), Grenoble 1991 
  7. Gauthier J. P., Bornard G., 10.1109/TAC.1981.1102743, IEEE Trans. Automat. Control 26 (1981), 922–926 (1981) Zbl0553.93014MR0635851DOI10.1109/TAC.1981.1102743
  8. Gauthier J. P., Kupka I., 10.1137/S0363012991221791, SIAM J. Control Optim. 32 (1994), 4, 974–994 (1994) Zbl0802.93008MR1280224DOI10.1137/S0363012991221791
  9. Glumineau A., Moog C. H., Plestan F., 10.1109/9.489283, IEEE Trans. Automat. Control 41 (1996), 598–603 (1996) Zbl0851.93018MR1385333DOI10.1109/9.489283
  10. Hammouri H., Gauthier, 10.1137/0330068, SIAM J. Control Optim. 30 (1992), 1295–1310 (1992) Zbl0771.93033MR1185623DOI10.1137/0330068
  11. Hammouri H., Morales J. De Leon, Observer Synthesis for state affine systems, In: Proc. 29th IEEE Conference on Decision and Control, Honolulu 1990, pp. 784–785 (1990) 
  12. Kang W., Krener A. J., Nonlinear asymptotic observer design: A backstepping approach, In: AFOSR Workshop on Dynamics Systems and Control, Pasadena, California 1998 
  13. Krener A. J., Isidori A., Linearization by output injection and nonlinear observers, Systems Control Lett. 3 (1983), 47–52 (1983) Zbl0524.93030MR0713426
  14. López–M. V., Morales, J. de Léon, Glumineau A., Transformation of nonlinear systems into state affine control systems and observer synthesis, In: IFAC CSSC, Nantes 1998, pp. 771–776 (1998) 
  15. López–M. V., Plestan, F., Glumineau A., Linearization by completely generalized input-output injection, Kybernetika 35 (1999), 6, 793–802 (1999) MR1747977
  16. Plestan F., Glumineau A., 10.1016/S0167-6911(97)00025-X, Systems Control Lett. 31 (1997), 115–128 (1997) Zbl0901.93013MR1461807DOI10.1016/S0167-6911(97)00025-X
  17. Souleiman I., Glumineau A., Constructive transformation of nonlinear systems into state affine MIMO form and nonlinear observers, Internat. J. Control. Submitted 
  18. Nijmeijer H., (eds.) T. I. Fossen, New Directions in Nonlinear Observer Design (Lecture Notes in Control and Inform, Sciences 244). Springer–Verlag, Berlin 1999 MR1699373
  19. Schaft A. J. Van der, 10.1016/0167-6911(89)90008-X, Systems Control Lett. 12 (1989), 151–160 (1989) MR0985565DOI10.1016/0167-6911(89)90008-X
  20. Xia X. H., Gao W. B., Nonlinear observer design by observer error linearization, SIAM J. Control Optim. 1 (1989), 199–216 (1989) Zbl0667.93014MR0980230

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