Improving the performance of semiglobal output controllers for nonlinear systems

Abdallah Benabdallah; Walid Hdidi

Kybernetika (2017)

  • Volume: 53, Issue: 2, page 296-330
  • ISSN: 0023-5954

Abstract

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For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers ( 𝒰 R ) R > 0 with increasing regions of attraction ( Ω R ) R > 0 is that, when the region of attraction Ω R is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is equal to some “fast” controller 𝒰 R 0 on a neighborhood of the origin. Under an input-output-to-state stability (IOSS) assumption, we propose a new semiglobal stabilizing hybrid feedback controller that unifies a “slow” controller that has a large region of attraction with a “fast” controller having a small region of attraction. This unification is inspired from the elegant hybrid unification of a local controller with a global one given in [21]. Moreover, this unification is different from the recent result [24], since in the cited paper the objective is just the stabilization; whereas in our study, the objective is the stabilization with high performance. Finally, we illustrate our main result by means of two numerical examples.

How to cite

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Benabdallah, Abdallah, and Hdidi, Walid. "Improving the performance of semiglobal output controllers for nonlinear systems." Kybernetika 53.2 (2017): 296-330. <http://eudml.org/doc/288195>.

@article{Benabdallah2017,
abstract = {For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers $(\mathcal \{U\}_R)_\{R>0\}$ with increasing regions of attraction $(\Omega _R)_\{R>0\}$ is that, when the region of attraction $\Omega _R$ is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is equal to some “fast” controller $\mathcal \{U\}_\{R_0\}$ on a neighborhood of the origin. Under an input-output-to-state stability (IOSS) assumption, we propose a new semiglobal stabilizing hybrid feedback controller that unifies a “slow” controller that has a large region of attraction with a “fast” controller having a small region of attraction. This unification is inspired from the elegant hybrid unification of a local controller with a global one given in [21]. Moreover, this unification is different from the recent result [24], since in the cited paper the objective is just the stabilization; whereas in our study, the objective is the stabilization with high performance. Finally, we illustrate our main result by means of two numerical examples.},
author = {Benabdallah, Abdallah, Hdidi, Walid},
journal = {Kybernetika},
keywords = {nonlinear system; hybrid output feedback; semiglobal output stabilization; local performance},
language = {eng},
number = {2},
pages = {296-330},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Improving the performance of semiglobal output controllers for nonlinear systems},
url = {http://eudml.org/doc/288195},
volume = {53},
year = {2017},
}

TY - JOUR
AU - Benabdallah, Abdallah
AU - Hdidi, Walid
TI - Improving the performance of semiglobal output controllers for nonlinear systems
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 2
SP - 296
EP - 330
AB - For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers $(\mathcal {U}_R)_{R>0}$ with increasing regions of attraction $(\Omega _R)_{R>0}$ is that, when the region of attraction $\Omega _R$ is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is equal to some “fast” controller $\mathcal {U}_{R_0}$ on a neighborhood of the origin. Under an input-output-to-state stability (IOSS) assumption, we propose a new semiglobal stabilizing hybrid feedback controller that unifies a “slow” controller that has a large region of attraction with a “fast” controller having a small region of attraction. This unification is inspired from the elegant hybrid unification of a local controller with a global one given in [21]. Moreover, this unification is different from the recent result [24], since in the cited paper the objective is just the stabilization; whereas in our study, the objective is the stabilization with high performance. Finally, we illustrate our main result by means of two numerical examples.
LA - eng
KW - nonlinear system; hybrid output feedback; semiglobal output stabilization; local performance
UR - http://eudml.org/doc/288195
ER -

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