Structurally stable design of output regulation for a class of nonlinear systems

Celia Villanueva-Novelo; Sergej Čelikovský; Bernardino Castillo-Toledo

Kybernetika (2001)

  • Volume: 37, Issue: 5, page [547]-564
  • ISSN: 0023-5954

Abstract

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The problem of output regulation of the systems affected by unknown constant parameters is considered here. The main goal is to find a unique feedback compensator (independent on the actual values of unknown parameters) that drives a given error (control criterion) asymptotically to zero for all values of parameters from a certain neighbourhood of their nominal value. Such a task is usually referred to as the structurally stable output regulation problem. Under certain assumptions, such a problem is known to be solvable using dynamical error feedback. The corresponding necessary and sufficient conditions basically include the solvability of the so-called regulator equation and the existence of an immersion of a certain system with outputs into the one having favourable observability and controllability properties. Its model is then directly used for dynamic compensator construction. Usually, such an immersion may be selected as the one to an observable linear system with outputs. In a general case, the above mentioned conditions are highly nonconstructive and difficult to check. This paper studies a certain particular class of systems, the so-called strictly triangular polynomial systems, where that immersion to a linear system can be obtained in a constructive way. Moreover, it provides computer algorithm (based on MAPLE symbolic package) to design the corresponding solution to the structurally stable output regulation problem. Examples together with computer simulations are included to clarify the suggested approach.

How to cite

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Villanueva-Novelo, Celia, Čelikovský, Sergej, and Castillo-Toledo, Bernardino. "Structurally stable design of output regulation for a class of nonlinear systems." Kybernetika 37.5 (2001): [547]-564. <http://eudml.org/doc/33550>.

@article{Villanueva2001,
abstract = {The problem of output regulation of the systems affected by unknown constant parameters is considered here. The main goal is to find a unique feedback compensator (independent on the actual values of unknown parameters) that drives a given error (control criterion) asymptotically to zero for all values of parameters from a certain neighbourhood of their nominal value. Such a task is usually referred to as the structurally stable output regulation problem. Under certain assumptions, such a problem is known to be solvable using dynamical error feedback. The corresponding necessary and sufficient conditions basically include the solvability of the so-called regulator equation and the existence of an immersion of a certain system with outputs into the one having favourable observability and controllability properties. Its model is then directly used for dynamic compensator construction. Usually, such an immersion may be selected as the one to an observable linear system with outputs. In a general case, the above mentioned conditions are highly nonconstructive and difficult to check. This paper studies a certain particular class of systems, the so-called strictly triangular polynomial systems, where that immersion to a linear system can be obtained in a constructive way. Moreover, it provides computer algorithm (based on MAPLE symbolic package) to design the corresponding solution to the structurally stable output regulation problem. Examples together with computer simulations are included to clarify the suggested approach.},
author = {Villanueva-Novelo, Celia, Čelikovský, Sergej, Castillo-Toledo, Bernardino},
journal = {Kybernetika},
keywords = {nonlinear system; stable output regulation; nonlinear system; stable output regulation},
language = {eng},
number = {5},
pages = {[547]-564},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Structurally stable design of output regulation for a class of nonlinear systems},
url = {http://eudml.org/doc/33550},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Villanueva-Novelo, Celia
AU - Čelikovský, Sergej
AU - Castillo-Toledo, Bernardino
TI - Structurally stable design of output regulation for a class of nonlinear systems
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 5
SP - [547]
EP - 564
AB - The problem of output regulation of the systems affected by unknown constant parameters is considered here. The main goal is to find a unique feedback compensator (independent on the actual values of unknown parameters) that drives a given error (control criterion) asymptotically to zero for all values of parameters from a certain neighbourhood of their nominal value. Such a task is usually referred to as the structurally stable output regulation problem. Under certain assumptions, such a problem is known to be solvable using dynamical error feedback. The corresponding necessary and sufficient conditions basically include the solvability of the so-called regulator equation and the existence of an immersion of a certain system with outputs into the one having favourable observability and controllability properties. Its model is then directly used for dynamic compensator construction. Usually, such an immersion may be selected as the one to an observable linear system with outputs. In a general case, the above mentioned conditions are highly nonconstructive and difficult to check. This paper studies a certain particular class of systems, the so-called strictly triangular polynomial systems, where that immersion to a linear system can be obtained in a constructive way. Moreover, it provides computer algorithm (based on MAPLE symbolic package) to design the corresponding solution to the structurally stable output regulation problem. Examples together with computer simulations are included to clarify the suggested approach.
LA - eng
KW - nonlinear system; stable output regulation; nonlinear system; stable output regulation
UR - http://eudml.org/doc/33550
ER -

References

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  4. Čelikovský S., Huang J., Continuous feedback practical output regulation for a class of nonlinear systems having nonstabilizable linearization, In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 2000, pp. 4796–4801 
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  8. Huang J., 10.1109/9.388697, IEEE Trans. Automat. Control 40 (1995), 1118–1122 (1995) MR1345975DOI10.1109/9.388697
  9. Isidori A., Nonlinear Control Systems, Third edition. Springer–Verlag, New York 1995, pp. 385–425 (1995) Zbl0878.93001MR1410988
  10. Isidori A., Byrnes C. I., 10.1109/9.45168, IEEE Trans. Automat. Control 35 (1990), 131–140 (1990) Zbl0704.93034MR1038409DOI10.1109/9.45168
  11. Knobloch H., al A. Isidori et, Topics in Control Theory, Birkhäuser, Boston 1993 Zbl0789.93073MR1284714
  12. Marino R., Tomei P., Nonlinear Control Design – Nonlinear, Robust and Adaptive, Prentice Hall, Englewood Cliffs, N.Y. 1994 

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