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Stochastic Approximation and Its Applications

  • Book
  • © 2002

Overview

Authors:
  1. Han-Fu Chen

    1. Institute of Systems Science Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, P.R. China

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Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 64)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xv
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  2. Robbins-Monro Algorithm

    Pages 1-24

  3. Stochastic Approximation Algorithms with Expanding Truncations

    Pages 25-93

  4. Asymptotic Properties of Stochastic Approximation Algorithms

    Pages 95-149

  5. Optimization by Stochastic Approximation

    Pages 151-218

  6. Application to Signal Processing

    Pages 219-288

  7. Application to Systems and Control

    Pages 289-328

  8. Back Matter

    Pages 329-359
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Keywords

About this book

Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e. , the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.

Authors and Affiliations

  • Institute of Systems Science Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, P.R. China

    Han-Fu Chen

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