From Data to Model
The problem of obtaining dynamical models directly from an observed time-series occurs in many fields of application. There are a number of possible approaches to this problem. In this volume a number of such points of view are exposed: the statistical ti
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FromData to Model With 35 Figures
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong
Professor Jan C. Willems Department of Mathematics University of Groningen P.O. Box 800 9700 AV Groningen The Netherlands
ISBN-13 :978-3-642-75009-0 e-ISBN-13 :978-3-642-75007-6 DOl: 10.1007/978-3-642-75007-6
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PREFACE
The problem of obtaining dynamical models directly from an observed time-series occurs in many fields of application. There are a number of possible approaches to this problem. In this volume a number of such points of view are exposed: the statistical time series approach, a theory of guaranted performance, and finally a deterministic approximation approach. This volume is an out-growth of a number of get-togethers sponsered by the Systems and Decision Sciences group of the International Institute of Applied Systems Analysis (IIASA) in Laxenburg, Austria. The hospitality and support of this organization is gratefully acknowledged.
Jan Willems Groningen, the Netherlands May 1989
TABLE OF CONTENTS
Linear System Identification- A Survey
page
1
M. Deistler A Tutorial on Hankel-Norm Approximation
26
K. Glover A Deterministic Approach to Approximate Modelling
49
C. Heij and J.C. Willems Identification - a Theory of Guaranteed Estimates
135
A.B. Kurzhanski Statistical Aspects of Model Selection
215
R. Shibata Index
241
Addresses of Authors
246
LINEAR SYSTEM IDENTIFICATION· A SURVEY M. DEISTLER
Abstract In
this paper we give an introductory survey on the theory of
identification of (in general MIMO) linear systems from (discrete) time series data. The main parts are: Structure theory for linear systems, asymptotic properties of maximum likelihood type estimators, estimation of the dynamic specification by methods based on information criteria and finally, extensions and alternative approaches such as identification of unstable systems and errors-in-variables.
Keywords Linear systems, parametrization, maximum likelihood estimation, information criteria, errors-in-variables.
2
1, INTRODUCTION The problem of deducing a good model from data is a central issue in many
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