WHEN IS ADAPTIVE BETTER THAN OPTIMAL

Authors
Citation
Jj. Fuchs et B. Delyon, WHEN IS ADAPTIVE BETTER THAN OPTIMAL, IEEE transactions on automatic control, 38(11), 1993, pp. 1700-1703
Citations number
11
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control","Engineering, Eletrical & Electronic
ISSN journal
00189286
Volume
38
Issue
11
Year of publication
1993
Pages
1700 - 1703
Database
ISI
SICI code
0018-9286(1993)38:11<1700:WIABTO>2.0.ZU;2-5
Abstract
Given a stationary process, let us predict it using a first-order pred ictor whose single coefficient is adapted to the current observations using a constant gain identification algorithm. We investigate the pre diction error variance as a function of the adaptation gain i.e., the length of the memory (the number of observations) of the identificatio n scheme. An infinite-memory corresponds to the asymptotically constan t optimal predictor and a finite memory to a locally adaptive time var ying predictor. We show that, in some specified situations, the predic tion error variance associated with the finite memory adaptation schem e is smaller that the optimal variance. This of course can only occur if the model is misspecified i.e., the structure of the optimal predic tor too simple.