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On minimax approach to non-parametric adaptive control

✍ Scribed by Anatoli Juditsky; Alexander Nazin

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 135 KB
Volume: 15
Category: Article
ISSN: 0890-6327
DOI: 10.1002/acs.648

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✦ Synopsis

Abstract

The subject of the paper is the adaptive stabilization problem for a functional autoregressive model. The uncertainty is represented by a class of functions satisfying the Hölder condition with given degree of smoothness s>0. We follow the information approach, first used in adaptive control problems by Nemirovsky and Tsypkin in 1984. We present the asymptotically minimax lower bounds for the mean‐square error of stabilization and provide a ‘quasi‐optimal’ adaptive control algorithm which attains the minimax rate of convergence up to a logarithmic factor. Copyright © 2001 John Wiley & Sons, Ltd.

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