Generalized immersion and nonlinear robust output regulation problem

Bernardino Castillo-Toledo; Sergej Čelikovský; S. Di Gennaro

Kybernetika (2004)

  • Volume: 40, Issue: 2, page [207]-220
  • ISSN: 0023-5954

Abstract

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The problem of output regulation of the system affected by unknown constant parameters is considered here. Under certain assumptions, such a problem is known to be solvable using error feedback via the so-called immersion to an observable linear system with outputs. Nevertheless, for many interesting cases this kind of finite dimensional immersion is difficult or even impossible to find. In order to achieve constructive procedures for wider classes, this paper investigates a more general type of immersion. Such a generalized immersion enables to solve robust output regulation problem via dynamic feedback compensator using error and exosystem state measurement. When the exosystem states are not completely measurable, a modified observed-based generalized immersion is then presented. The main result obtained here is that under reasonable assumptions both the full and partial exosystem measurement problems are equivalently solvable. Examples together with computer simulation are included to clarify the suggested approach.

How to cite

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Castillo-Toledo, Bernardino, Čelikovský, Sergej, and Di Gennaro, S.. "Generalized immersion and nonlinear robust output regulation problem." Kybernetika 40.2 (2004): [207]-220. <http://eudml.org/doc/33695>.

@article{Castillo2004,
abstract = {The problem of output regulation of the system affected by unknown constant parameters is considered here. Under certain assumptions, such a problem is known to be solvable using error feedback via the so-called immersion to an observable linear system with outputs. Nevertheless, for many interesting cases this kind of finite dimensional immersion is difficult or even impossible to find. In order to achieve constructive procedures for wider classes, this paper investigates a more general type of immersion. Such a generalized immersion enables to solve robust output regulation problem via dynamic feedback compensator using error and exosystem state measurement. When the exosystem states are not completely measurable, a modified observed-based generalized immersion is then presented. The main result obtained here is that under reasonable assumptions both the full and partial exosystem measurement problems are equivalently solvable. Examples together with computer simulation are included to clarify the suggested approach.},
author = {Castillo-Toledo, Bernardino, Čelikovský, Sergej, Di Gennaro, S.},
journal = {Kybernetika},
keywords = {output regulation; robust; nonlinear; immersion; output regulation; robust control; nonlinear system; immersion},
language = {eng},
number = {2},
pages = {[207]-220},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Generalized immersion and nonlinear robust output regulation problem},
url = {http://eudml.org/doc/33695},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Castillo-Toledo, Bernardino
AU - Čelikovský, Sergej
AU - Di Gennaro, S.
TI - Generalized immersion and nonlinear robust output regulation problem
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 2
SP - [207]
EP - 220
AB - The problem of output regulation of the system affected by unknown constant parameters is considered here. Under certain assumptions, such a problem is known to be solvable using error feedback via the so-called immersion to an observable linear system with outputs. Nevertheless, for many interesting cases this kind of finite dimensional immersion is difficult or even impossible to find. In order to achieve constructive procedures for wider classes, this paper investigates a more general type of immersion. Such a generalized immersion enables to solve robust output regulation problem via dynamic feedback compensator using error and exosystem state measurement. When the exosystem states are not completely measurable, a modified observed-based generalized immersion is then presented. The main result obtained here is that under reasonable assumptions both the full and partial exosystem measurement problems are equivalently solvable. Examples together with computer simulation are included to clarify the suggested approach.
LA - eng
KW - output regulation; robust; nonlinear; immersion; output regulation; robust control; nonlinear system; immersion
UR - http://eudml.org/doc/33695
ER -

References

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  1. Byrnes C. I., Priscolli, F. Delli, Isidori A., Output regulation of uncertain nonlinear systems, Birkhäuser, Boston 1997 MR1438783
  2. Čelikovský S., Huang J., Continuous feedback asymptotic output regulation for a class of nonlinear systems having nonstabilizable linearization, Proc. 37th IEEE Conference on Decision and Control, Tampa, Florida, 1999, pp. 3087–3092 (1999) 
  3. Čelikovský S., Huang J., Continuous feedback practical output regulation for a class of nonlinear systems having nonstabilizable linearization, Proc. 38th IEEE Conference on Decision and Control, Phoenix, Arizona, 2000, pp. 4796–4801 
  4. Čelikovský S., Villanueva-Novelo, C., Castillo-Toledo B., Robust output regulation for nonlinear systems via generalized immersion, Proc. Conference on Systems, Cybernetics and Informatics, IX, Orlando, Flo. USA, 2000, pp. 96–101 
  5. Hepburn J. S. A., Wonham W. M., 10.1109/TAC.1984.1103563, IEEE Trans. Automat. Control 29 (1984), 397–403 (1984) MR0748204DOI10.1109/TAC.1984.1103563
  6. Huang J., Rugh W. J., 10.1016/0005-1098(90)90081-R, Automatica 26 (1990), 963–972 (1990) Zbl0717.93019MR1080983DOI10.1016/0005-1098(90)90081-R
  7. Huang J., 10.1109/9.388697, IEEE Trans. Automat. Control 40 (1995), 1118–1122 (1995) MR1345975DOI10.1109/9.388697
  8. Isidori A., Byrnes C. I., 10.1109/9.45168, IEEE Trans. Automat. Control 35 (1990), 131–140 (1990) Zbl0704.93034MR1038409DOI10.1109/9.45168
  9. Isidori A., Nonlinear Control Systems, Third edition. Springer–Verlag, London 1995 Zbl0931.93005MR1410988

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