Asymptotic performance guarantees in adaptive control

Konstantinos Tsakalis, Suttipan Limanond

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper we address the problem of improving the asymptotic performance guarantees of a class of model reference adaptive controllers under insufficient excitation and in the presence of perturbations such as non-parametric uncertainty and bounded disturbances. We show that for a class of perturbations whose normalized effect is bounded by an a priori known function of time an estimate of the parametric uncertainty set can be obtained on-line via a set membership estimator. Furthermore, by incorporating this estimate as an additional constraint in the adaptive law generating the controller parameters, we show that the resulting adaptive controller offers dead-zone-like performance guarantees in the lim-sup sense while preserving the desirable root-mean-square performance guarantees of gradient-based algorithms.

Original languageEnglish (US)
Pages (from-to)173-199
Number of pages27
JournalInternational Journal of Adaptive Control and Signal Processing
Volume8
Issue number2
StatePublished - Mar 1994

Fingerprint

Controllers
Uncertainty

ASJC Scopus subject areas

  • Signal Processing
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

Asymptotic performance guarantees in adaptive control. / Tsakalis, Konstantinos; Limanond, Suttipan.

In: International Journal of Adaptive Control and Signal Processing, Vol. 8, No. 2, 03.1994, p. 173-199.

Research output: Contribution to journalArticle

@article{c1d23719f57748dbb1e298bc1edd71b5,
title = "Asymptotic performance guarantees in adaptive control",
abstract = "In this paper we address the problem of improving the asymptotic performance guarantees of a class of model reference adaptive controllers under insufficient excitation and in the presence of perturbations such as non-parametric uncertainty and bounded disturbances. We show that for a class of perturbations whose normalized effect is bounded by an a priori known function of time an estimate of the parametric uncertainty set can be obtained on-line via a set membership estimator. Furthermore, by incorporating this estimate as an additional constraint in the adaptive law generating the controller parameters, we show that the resulting adaptive controller offers dead-zone-like performance guarantees in the lim-sup sense while preserving the desirable root-mean-square performance guarantees of gradient-based algorithms.",
author = "Konstantinos Tsakalis and Suttipan Limanond",
year = "1994",
month = "3",
language = "English (US)",
volume = "8",
pages = "173--199",
journal = "International Journal of Adaptive Control and Signal Processing",
issn = "0890-6327",
publisher = "John Wiley and Sons Ltd",
number = "2",

}

TY - JOUR

T1 - Asymptotic performance guarantees in adaptive control

AU - Tsakalis, Konstantinos

AU - Limanond, Suttipan

PY - 1994/3

Y1 - 1994/3

N2 - In this paper we address the problem of improving the asymptotic performance guarantees of a class of model reference adaptive controllers under insufficient excitation and in the presence of perturbations such as non-parametric uncertainty and bounded disturbances. We show that for a class of perturbations whose normalized effect is bounded by an a priori known function of time an estimate of the parametric uncertainty set can be obtained on-line via a set membership estimator. Furthermore, by incorporating this estimate as an additional constraint in the adaptive law generating the controller parameters, we show that the resulting adaptive controller offers dead-zone-like performance guarantees in the lim-sup sense while preserving the desirable root-mean-square performance guarantees of gradient-based algorithms.

AB - In this paper we address the problem of improving the asymptotic performance guarantees of a class of model reference adaptive controllers under insufficient excitation and in the presence of perturbations such as non-parametric uncertainty and bounded disturbances. We show that for a class of perturbations whose normalized effect is bounded by an a priori known function of time an estimate of the parametric uncertainty set can be obtained on-line via a set membership estimator. Furthermore, by incorporating this estimate as an additional constraint in the adaptive law generating the controller parameters, we show that the resulting adaptive controller offers dead-zone-like performance guarantees in the lim-sup sense while preserving the desirable root-mean-square performance guarantees of gradient-based algorithms.

UR - http://www.scopus.com/inward/record.url?scp=0028396514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028396514&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0028396514

VL - 8

SP - 173

EP - 199

JO - International Journal of Adaptive Control and Signal Processing

JF - International Journal of Adaptive Control and Signal Processing

SN - 0890-6327

IS - 2

ER -