Exponential convergence of recursive least squares with exponential forgetting factor

Richard Johnstone; C Richard Johnson; Robert R. Bitmead; Brian Anderson

doi:10.1109/CDC.1982.268295

Exponential convergence of recursive least squares with exponential forgetting factor

Richard Johnstone, C Richard Johnson, Robert R. Bitmead, Brian Anderson

School of Engineering

Research output: Contribution to conference › Paper › peer-review

Abstract

This paper demonstrates that, provided the system input is persistently exciting, the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent. Further, it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary. The result holds for stable finite-dimensional, linear, time-invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail.

Original language	English
Pages	994-997
Number of pages	4
DOIs	https://doi.org/10.1109/CDC.1982.268295
Publication status	Published - 1982
Event	21st IEEE Conference on Decision and Control - Holiday Inn-International Drive, Orlando, United States Duration: 8 Dec 1982 → 10 Dec 1982

Conference

Conference	21st IEEE Conference on Decision and Control
Country/Territory	United States
City	Orlando
Period	8/12/82 → 10/12/82

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10.1109/CDC.1982.268295

Cite this

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title = "Exponential convergence of recursive least squares with exponential forgetting factor",

abstract = "This paper demonstrates that, provided the system input is persistently exciting, the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent. Further, it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary. The result holds for stable finite-dimensional, linear, time-invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail.",

author = "Richard Johnstone and Johnson, {C Richard} and Bitmead, {Robert R.} and Brian Anderson",

year = "1982",

doi = "10.1109/CDC.1982.268295",

language = "English",

pages = "994--997",

note = "21st IEEE Conference on Decision and Control ; Conference date: 08-12-1982 Through 10-12-1982",

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TY - CONF

T1 - Exponential convergence of recursive least squares with exponential forgetting factor

AU - Johnstone, Richard

AU - Johnson, C Richard

AU - Bitmead, Robert R.

AU - Anderson, Brian

PY - 1982

Y1 - 1982

N2 - This paper demonstrates that, provided the system input is persistently exciting, the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent. Further, it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary. The result holds for stable finite-dimensional, linear, time-invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail.

AB - This paper demonstrates that, provided the system input is persistently exciting, the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent. Further, it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary. The result holds for stable finite-dimensional, linear, time-invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail.

U2 - 10.1109/CDC.1982.268295

DO - 10.1109/CDC.1982.268295

M3 - Paper

SP - 994

EP - 997

T2 - 21st IEEE Conference on Decision and Control

Y2 - 8 December 1982 through 10 December 1982

ER -

Exponential convergence of recursive least squares with exponential forgetting factor

Abstract

Conference

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