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Exponential convergence of recursive least squares with exponential forgetting factor

✍ Scribed by Richard M. Johnstone; C. Richard Johnson Jr.; Robert R. Bitmead; Brian D.O. Anderson

Publisher: Elsevier Science
Year: 1982
Tongue: English
Weight: 401 KB
Volume: 2
Category: Article
ISSN: 0167-6911
DOI: 10.1016/s0167-6911(82)80014-5

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✦ Synopsis

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.

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