On certain performance issues arising in adaptive control

Konstantinos Tsakalis, Suttipar Limanond

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this note we address the problem of improving the performance of a class of Model Reference. Adaptive Controllers (MRAC) under insufficient excitation and in the presence of perturbations, e.g., non-parametric uncertainty and bounded disturbances. In such an environment, the global boundedness of a MRAC closed-loop (BIBO stability) has been established, without any excitation requirements, for both bounded disturbances and 'small' non-parametric uncertainty (e.g., see [1,2] and references therein). In addition to this form of robust stability, the adaptive controller also guarantees robust tracking performance in a root-mean-square (RMS) sense. That is, the RMS value of the normalized tracking error is of order of the size of the non-parametric uncertainty and/or the RMS value of the external disturbances. Unfortunately, however, this weak performance measure is rarely reliable in assessing the effectiveness of the adaptive controller. Indeed, in the absence of sufficient excitation, even arbitrarily small perturbations may cause the adjustable parameters to drift away from their desired or actual values. Such a parameter drift can then produce large instantaneous tracking errors due to either a change in the excitation signal or the (local) destabilization of the closed loop system. This type of undesirable behavior, often referred to as burst phenomena, has been the subject of several studies (e.g., see [3, 4, 5, 6]). A typical remedy of the bursting problem has been recognized in the form of absolute or relative dead-zones [7,8]. The main idea of this approach is to cease adaptation when the estimation error becomes smaller than a threshold, derived as a conservative estimate of the worst-case upper bound of the perturbation entering the estimation algorithm of the adaptive controller. The net result of this approach is that if the threshold is chosen appropriately, the estimated parameters converge and the tracking error enters a residual set where its magnitude is proportional to the dead-zone threshold. We refer to this type of performance characterization as performance in a lim sup sense. Thus, for adaptive laws with dead-zone both the RMS and lim sup values of the tracking error are of the order of the threshold. (In the relative dead-zone case, all quantities are suitably normalized while the threshold should be sufficiently small to guarantee the BIBO stability of the closed-loop). The need for a conservative selection of the dead-zone threshold, however, constitutes the main drawback of this approach in the sense that if the threshold is grossly overestimated, the RMS tracking performance may deteriorate unnecessarily.

Original languageEnglish (US)
Title of host publicationAmerican Control Conference
Editors Anon
Place of PublicationPiscataway, NJ, United States
PublisherPubl by IEEE
Pages287-288
Number of pages2
ISBN (Print)0780308611
StatePublished - 1993
EventProceedings of the 1993 American Control Conference Part 3 (of 3) - San Francisco, CA, USA
Duration: Jun 2 1993Jun 4 1993

Other

OtherProceedings of the 1993 American Control Conference Part 3 (of 3)
CitySan Francisco, CA, USA
Period6/2/936/4/93

Fingerprint

Controllers
Closed loop systems
Error analysis
Uncertainty
Robust stability

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Tsakalis, K., & Limanond, S. (1993). On certain performance issues arising in adaptive control. In Anon (Ed.), American Control Conference (pp. 287-288). Piscataway, NJ, United States: Publ by IEEE.

On certain performance issues arising in adaptive control. / Tsakalis, Konstantinos; Limanond, Suttipar.

American Control Conference. ed. / Anon. Piscataway, NJ, United States : Publ by IEEE, 1993. p. 287-288.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Tsakalis, K & Limanond, S 1993, On certain performance issues arising in adaptive control. in Anon (ed.), American Control Conference. Publ by IEEE, Piscataway, NJ, United States, pp. 287-288, Proceedings of the 1993 American Control Conference Part 3 (of 3), San Francisco, CA, USA, 6/2/93.
Tsakalis K, Limanond S. On certain performance issues arising in adaptive control. In Anon, editor, American Control Conference. Piscataway, NJ, United States: Publ by IEEE. 1993. p. 287-288
Tsakalis, Konstantinos ; Limanond, Suttipar. / On certain performance issues arising in adaptive control. American Control Conference. editor / Anon. Piscataway, NJ, United States : Publ by IEEE, 1993. pp. 287-288
@inproceedings{959a19ac69d84db5ae3b44f5b2774bd4,
title = "On certain performance issues arising in adaptive control",
abstract = "In this note we address the problem of improving the performance of a class of Model Reference. Adaptive Controllers (MRAC) under insufficient excitation and in the presence of perturbations, e.g., non-parametric uncertainty and bounded disturbances. In such an environment, the global boundedness of a MRAC closed-loop (BIBO stability) has been established, without any excitation requirements, for both bounded disturbances and 'small' non-parametric uncertainty (e.g., see [1,2] and references therein). In addition to this form of robust stability, the adaptive controller also guarantees robust tracking performance in a root-mean-square (RMS) sense. That is, the RMS value of the normalized tracking error is of order of the size of the non-parametric uncertainty and/or the RMS value of the external disturbances. Unfortunately, however, this weak performance measure is rarely reliable in assessing the effectiveness of the adaptive controller. Indeed, in the absence of sufficient excitation, even arbitrarily small perturbations may cause the adjustable parameters to drift away from their desired or actual values. Such a parameter drift can then produce large instantaneous tracking errors due to either a change in the excitation signal or the (local) destabilization of the closed loop system. This type of undesirable behavior, often referred to as burst phenomena, has been the subject of several studies (e.g., see [3, 4, 5, 6]). A typical remedy of the bursting problem has been recognized in the form of absolute or relative dead-zones [7,8]. The main idea of this approach is to cease adaptation when the estimation error becomes smaller than a threshold, derived as a conservative estimate of the worst-case upper bound of the perturbation entering the estimation algorithm of the adaptive controller. The net result of this approach is that if the threshold is chosen appropriately, the estimated parameters converge and the tracking error enters a residual set where its magnitude is proportional to the dead-zone threshold. We refer to this type of performance characterization as performance in a lim sup sense. Thus, for adaptive laws with dead-zone both the RMS and lim sup values of the tracking error are of the order of the threshold. (In the relative dead-zone case, all quantities are suitably normalized while the threshold should be sufficiently small to guarantee the BIBO stability of the closed-loop). The need for a conservative selection of the dead-zone threshold, however, constitutes the main drawback of this approach in the sense that if the threshold is grossly overestimated, the RMS tracking performance may deteriorate unnecessarily.",
author = "Konstantinos Tsakalis and Suttipar Limanond",
year = "1993",
language = "English (US)",
isbn = "0780308611",
pages = "287--288",
editor = "Anon",
booktitle = "American Control Conference",
publisher = "Publ by IEEE",

}

TY - GEN

T1 - On certain performance issues arising in adaptive control

AU - Tsakalis, Konstantinos

AU - Limanond, Suttipar

PY - 1993

Y1 - 1993

N2 - In this note we address the problem of improving the performance of a class of Model Reference. Adaptive Controllers (MRAC) under insufficient excitation and in the presence of perturbations, e.g., non-parametric uncertainty and bounded disturbances. In such an environment, the global boundedness of a MRAC closed-loop (BIBO stability) has been established, without any excitation requirements, for both bounded disturbances and 'small' non-parametric uncertainty (e.g., see [1,2] and references therein). In addition to this form of robust stability, the adaptive controller also guarantees robust tracking performance in a root-mean-square (RMS) sense. That is, the RMS value of the normalized tracking error is of order of the size of the non-parametric uncertainty and/or the RMS value of the external disturbances. Unfortunately, however, this weak performance measure is rarely reliable in assessing the effectiveness of the adaptive controller. Indeed, in the absence of sufficient excitation, even arbitrarily small perturbations may cause the adjustable parameters to drift away from their desired or actual values. Such a parameter drift can then produce large instantaneous tracking errors due to either a change in the excitation signal or the (local) destabilization of the closed loop system. This type of undesirable behavior, often referred to as burst phenomena, has been the subject of several studies (e.g., see [3, 4, 5, 6]). A typical remedy of the bursting problem has been recognized in the form of absolute or relative dead-zones [7,8]. The main idea of this approach is to cease adaptation when the estimation error becomes smaller than a threshold, derived as a conservative estimate of the worst-case upper bound of the perturbation entering the estimation algorithm of the adaptive controller. The net result of this approach is that if the threshold is chosen appropriately, the estimated parameters converge and the tracking error enters a residual set where its magnitude is proportional to the dead-zone threshold. We refer to this type of performance characterization as performance in a lim sup sense. Thus, for adaptive laws with dead-zone both the RMS and lim sup values of the tracking error are of the order of the threshold. (In the relative dead-zone case, all quantities are suitably normalized while the threshold should be sufficiently small to guarantee the BIBO stability of the closed-loop). The need for a conservative selection of the dead-zone threshold, however, constitutes the main drawback of this approach in the sense that if the threshold is grossly overestimated, the RMS tracking performance may deteriorate unnecessarily.

AB - In this note we address the problem of improving the performance of a class of Model Reference. Adaptive Controllers (MRAC) under insufficient excitation and in the presence of perturbations, e.g., non-parametric uncertainty and bounded disturbances. In such an environment, the global boundedness of a MRAC closed-loop (BIBO stability) has been established, without any excitation requirements, for both bounded disturbances and 'small' non-parametric uncertainty (e.g., see [1,2] and references therein). In addition to this form of robust stability, the adaptive controller also guarantees robust tracking performance in a root-mean-square (RMS) sense. That is, the RMS value of the normalized tracking error is of order of the size of the non-parametric uncertainty and/or the RMS value of the external disturbances. Unfortunately, however, this weak performance measure is rarely reliable in assessing the effectiveness of the adaptive controller. Indeed, in the absence of sufficient excitation, even arbitrarily small perturbations may cause the adjustable parameters to drift away from their desired or actual values. Such a parameter drift can then produce large instantaneous tracking errors due to either a change in the excitation signal or the (local) destabilization of the closed loop system. This type of undesirable behavior, often referred to as burst phenomena, has been the subject of several studies (e.g., see [3, 4, 5, 6]). A typical remedy of the bursting problem has been recognized in the form of absolute or relative dead-zones [7,8]. The main idea of this approach is to cease adaptation when the estimation error becomes smaller than a threshold, derived as a conservative estimate of the worst-case upper bound of the perturbation entering the estimation algorithm of the adaptive controller. The net result of this approach is that if the threshold is chosen appropriately, the estimated parameters converge and the tracking error enters a residual set where its magnitude is proportional to the dead-zone threshold. We refer to this type of performance characterization as performance in a lim sup sense. Thus, for adaptive laws with dead-zone both the RMS and lim sup values of the tracking error are of the order of the threshold. (In the relative dead-zone case, all quantities are suitably normalized while the threshold should be sufficiently small to guarantee the BIBO stability of the closed-loop). The need for a conservative selection of the dead-zone threshold, however, constitutes the main drawback of this approach in the sense that if the threshold is grossly overestimated, the RMS tracking performance may deteriorate unnecessarily.

UR - http://www.scopus.com/inward/record.url?scp=0027845870&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027845870&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0780308611

SP - 287

EP - 288

BT - American Control Conference

A2 - Anon, null

PB - Publ by IEEE

CY - Piscataway, NJ, United States

ER -