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Approximate and Noisy Realization of Discrete-Time Dynamical Systems

  • Authors
  • Yasumichi¬†Hasegawa
Book

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 376)

Table of contents

  1. Front Matter
  2. Yasumichi Hasegawa
    Pages 1-6
  3. Yasumichi Hasegawa
    Pages 7-13
  4. Back Matter

About this book

Introduction

This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relations. It will be of special interest to researchers, engineers and graduate students who have specialized in ?ltering theory and system theory. From noisy or noiseless data, reductionwillbemade.Anewmethodwhichreducesnoiseormodelsinformation will be proposed. Using this method will allow model description to be treated as noise reduction or model reduction. As proof of the e?cacy, this monograph provides new results and their extensions which can also be applied to nonlinear dynamical systems. To present the e?ectiveness of our method, many actual examples of noise and model information reduction will also be provided. Using the analysis of state space approach, the model reduction problem may have become a major theme of technology after 1966 for emphasizing e?ciency in the ?elds of control, economy, numerical analysis, and others. Noise reduction problems in the analysis of noisy dynamical systems may havebecomeamajorthemeoftechnologyafter1974foremphasizinge?ciencyin control.However,thesubjectsoftheseresearcheshavebeenmainlyconcentrated in linear systems. In common model reduction of linear systems in use today, a singular value decompositionofaHankelmatrixisusedto?ndareducedordermodel.However, the existence of the conditions of the reduced order model are derived without evaluationoftheresultantmodel.Inthecommontypicalnoisereductionoflinear systems in use today, the order and parameters of the systems are determined by minimizing information criterion. Approximate and noisy realization problems for input/output relations can be roughly stated as follows: A. The approximate realization problem. For any input/output map, ?nd one mathematical model such that it is similar totheinput/outputmapandhasalowerdimensionthanthegivenminimalstate spaceofadynamicalsystemwhichhasthesamebehaviortotheinput/outputmap. B. The noisy realization problem.

Keywords

Additive Noise Discrete-Time Dynamical Systems Linear Systems filtering system system theory systems theory

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-79434-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-540-79433-2
  • Online ISBN 978-3-540-79434-9
  • Series Print ISSN 0170-8643
  • Series Online ISSN 1610-7411
  • Buy this book on publisher's site
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