A sample-time adjusted feedback for robust bounded output stabilization

Patricio Ordaz; Hussain Alazki; Alexander Poznyak

Kybernetika (2013)

  • Volume: 49, Issue: 6, page 911-934
  • ISSN: 0023-5954

Abstract

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This paper deals with a bounded control design for a class of nonlinear systems where the mathematical model may be not explicitly given. This class of uncertain nonlinear systems governed by a system of ODE with quasi-Lipschitz right-hand side and containing external perturbations as well. The Attractive Ellipsoid Method (AEM) application permits to describe the class of nonlinear feedbacks (containing a nonlinear projection operator, a linear state estimator and a feedback matrix-gain) guaranteeing a boundedness of all possible trajectories around the origin. To fulfill this property some modification of AEM are introduced: basically, some sort of sample-time corrections of the feedback parameters are required. The optimization of feedback within this class of controllers is associated with the selection of the feedback parameters which provide the trajectory converges within an ellipsoid of a “minimal size“. The effectiveness of the suggested approach is illustrated by its application to a flexible arm system).

How to cite

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Ordaz, Patricio, Alazki, Hussain, and Poznyak, Alexander. "A sample-time adjusted feedback for robust bounded output stabilization." Kybernetika 49.6 (2013): 911-934. <http://eudml.org/doc/260807>.

@article{Ordaz2013,
abstract = {This paper deals with a bounded control design for a class of nonlinear systems where the mathematical model may be not explicitly given. This class of uncertain nonlinear systems governed by a system of ODE with quasi-Lipschitz right-hand side and containing external perturbations as well. The Attractive Ellipsoid Method (AEM) application permits to describe the class of nonlinear feedbacks (containing a nonlinear projection operator, a linear state estimator and a feedback matrix-gain) guaranteeing a boundedness of all possible trajectories around the origin. To fulfill this property some modification of AEM are introduced: basically, some sort of sample-time corrections of the feedback parameters are required. The optimization of feedback within this class of controllers is associated with the selection of the feedback parameters which provide the trajectory converges within an ellipsoid of a “minimal size“. The effectiveness of the suggested approach is illustrated by its application to a flexible arm system).},
author = {Ordaz, Patricio, Alazki, Hussain, Poznyak, Alexander},
journal = {Kybernetika},
keywords = {sample-time data; attractive ellipsoid; state estimation; saturated control process; flexible arm system; sample-time data; attractive ellipsoid; state estimation; saturated control process; flexible arm system},
language = {eng},
number = {6},
pages = {911-934},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A sample-time adjusted feedback for robust bounded output stabilization},
url = {http://eudml.org/doc/260807},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Ordaz, Patricio
AU - Alazki, Hussain
AU - Poznyak, Alexander
TI - A sample-time adjusted feedback for robust bounded output stabilization
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 6
SP - 911
EP - 934
AB - This paper deals with a bounded control design for a class of nonlinear systems where the mathematical model may be not explicitly given. This class of uncertain nonlinear systems governed by a system of ODE with quasi-Lipschitz right-hand side and containing external perturbations as well. The Attractive Ellipsoid Method (AEM) application permits to describe the class of nonlinear feedbacks (containing a nonlinear projection operator, a linear state estimator and a feedback matrix-gain) guaranteeing a boundedness of all possible trajectories around the origin. To fulfill this property some modification of AEM are introduced: basically, some sort of sample-time corrections of the feedback parameters are required. The optimization of feedback within this class of controllers is associated with the selection of the feedback parameters which provide the trajectory converges within an ellipsoid of a “minimal size“. The effectiveness of the suggested approach is illustrated by its application to a flexible arm system).
LA - eng
KW - sample-time data; attractive ellipsoid; state estimation; saturated control process; flexible arm system; sample-time data; attractive ellipsoid; state estimation; saturated control process; flexible arm system
UR - http://eudml.org/doc/260807
ER -

References

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