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Bias, Variance and Optimal Experiment Design: Some Comments on Closed Loop Identification
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1999 (English)Report (Other academic)
Abstract [en]

In this contribution we shall describe a rather unified way of expressing bias and variance in prediction error estimates. Theemphasis is on systems operating in closed loop. We shall describe the identification criterion function in the frequencydomain. The crucial entity is the joint spectrum of input and noise source. Different factorizations of this spectrum give differentinsights into the bias mechanisms of closed loop identification. It will be shown that so called {em indirect identification} is theanswer to the question of how to obtain consistent estimates of the dynamics part, even with an erroneous noise model. Wealso consider optimal design of experiments that seek to minimize the weighted variance of the dynamics estimate. It is shownthat open loop experiments are optimal if the input power is constrained. However for any criteria that involve any kind ofconstraints on the output power, closed loop experiments will be optimal. The optimal regulator does not depend on theweighting function in the criterion to be minimized.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1999. , 13 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2100
Keyword [en]
Closed loop identification
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55693ISRN: LiTH-ISY-R-2100OAI: oai:DiVA.org:liu-55693DiVA: diva2:316459
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-08Bibliographically approved

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Ljung, Lennart

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Citation style
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