Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems

Hazem N. Nounou

doi:10.1109/CDC.2003.1273064

Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems

Hazem N. Nounou^*

^*Corresponding author for this work

United Arab Emirates University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

In adaptive control algorithms, the adaptation routine (e.g., least squares or gradient) is usually used to adjust the controller parameters to approximate the ideal controller that is assumed to exist. Searching for the ideal parameter vector, a gradient-based hybrid adaptive routine is used here for continuous-time nonlinear systems. The adjustment of the parameter vector is usually based on minimizing the squared error. For direct adaptive control, in this paper an algorithm is presented to adapt the direction of the search vector so that the instantaneous control energy is minimized. Hence, the overall adaptive routine minimizes not only the squares error but also the instantaneous control energy. Stability results of the presented algorithm show that boundedness of the error is dependent on the length of the search vector.

Original language	English
Title of host publication	42nd IEEE International Conference on Decision and Control, CDC 2003 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2890-2895
Number of pages	6
ISBN (Print)	0780379241
DOIs	https://doi.org/10.1109/CDC.2003.1273064
Publication status	Published - 2003
Externally published	Yes
Event	42nd IEEE International Conference on Decision and Control, CDC 2003 - Maui, HI, United States Duration: 9 Dec 2003 → 12 Dec 2003

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	3
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	42nd IEEE International Conference on Decision and Control, CDC 2003
Country/Territory	United States
City	Maui, HI
Period	9/12/03 → 12/12/03

Access to Document

10.1109/CDC.2003.1273064

Cite this

Nounou, H. N. (2003). Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems. In 42nd IEEE International Conference on Decision and Control, CDC 2003 - Proceedings (pp. 2890-2895). (Proceedings of the IEEE Conference on Decision and Control; Vol. 3). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2003.1273064

@inproceedings{ee998ee63aae49578228a1ab2b35f1b3,

title = "Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems",

abstract = "In adaptive control algorithms, the adaptation routine (e.g., least squares or gradient) is usually used to adjust the controller parameters to approximate the ideal controller that is assumed to exist. Searching for the ideal parameter vector, a gradient-based hybrid adaptive routine is used here for continuous-time nonlinear systems. The adjustment of the parameter vector is usually based on minimizing the squared error. For direct adaptive control, in this paper an algorithm is presented to adapt the direction of the search vector so that the instantaneous control energy is minimized. Hence, the overall adaptive routine minimizes not only the squares error but also the instantaneous control energy. Stability results of the presented algorithm show that boundedness of the error is dependent on the length of the search vector.",

author = "Nounou, \{Hazem N.\}",

year = "2003",

doi = "10.1109/CDC.2003.1273064",

language = "English",

isbn = "0780379241",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "2890--2895",

booktitle = "42nd IEEE International Conference on Decision and Control, CDC 2003 - Proceedings",

address = "United States",

note = "42nd IEEE International Conference on Decision and Control, CDC 2003 ; Conference date: 09-12-2003 Through 12-12-2003",

}

Nounou, HN 2003, Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems. in 42nd IEEE International Conference on Decision and Control, CDC 2003 - Proceedings. Proceedings of the IEEE Conference on Decision and Control, vol. 3, Institute of Electrical and Electronics Engineers Inc., pp. 2890-2895, 42nd IEEE International Conference on Decision and Control, CDC 2003, Maui, HI, United States, 9/12/03. https://doi.org/10.1109/CDC.2003.1273064

Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems. / Nounou, Hazem N.
42nd IEEE International Conference on Decision and Control, CDC 2003 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2003. p. 2890-2895 (Proceedings of the IEEE Conference on Decision and Control; Vol. 3).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems

AU - Nounou, Hazem N.

PY - 2003

Y1 - 2003

N2 - In adaptive control algorithms, the adaptation routine (e.g., least squares or gradient) is usually used to adjust the controller parameters to approximate the ideal controller that is assumed to exist. Searching for the ideal parameter vector, a gradient-based hybrid adaptive routine is used here for continuous-time nonlinear systems. The adjustment of the parameter vector is usually based on minimizing the squared error. For direct adaptive control, in this paper an algorithm is presented to adapt the direction of the search vector so that the instantaneous control energy is minimized. Hence, the overall adaptive routine minimizes not only the squares error but also the instantaneous control energy. Stability results of the presented algorithm show that boundedness of the error is dependent on the length of the search vector.

AB - In adaptive control algorithms, the adaptation routine (e.g., least squares or gradient) is usually used to adjust the controller parameters to approximate the ideal controller that is assumed to exist. Searching for the ideal parameter vector, a gradient-based hybrid adaptive routine is used here for continuous-time nonlinear systems. The adjustment of the parameter vector is usually based on minimizing the squared error. For direct adaptive control, in this paper an algorithm is presented to adapt the direction of the search vector so that the instantaneous control energy is minimized. Hence, the overall adaptive routine minimizes not only the squares error but also the instantaneous control energy. Stability results of the presented algorithm show that boundedness of the error is dependent on the length of the search vector.

UR - https://www.scopus.com/pages/publications/1542348659

U2 - 10.1109/CDC.2003.1273064

DO - 10.1109/CDC.2003.1273064

M3 - Conference contribution

AN - SCOPUS:1542348659

SN - 0780379241

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2890

EP - 2895

BT - 42nd IEEE International Conference on Decision and Control, CDC 2003 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 42nd IEEE International Conference on Decision and Control, CDC 2003

Y2 - 9 December 2003 through 12 December 2003

ER -

Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems

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