Skip to main content

Stochastic Approximation Under Dependent Noises, Detecting Signals and Adaptive Control

  • Chapter

Abstract

Let f α(θ) be a family of unknown functions from a set into ℝ1, be a random parameter with the distribution Pα and with the mean value. The function is assumed to have unique minimum in at an internal point θ*.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Barabanov A.Ye., Granichin O.N., 1984, Optimal controller for a linear plant with bounded noise. Automat. Remote Control, 45, No.5, part 1, 578–584.

    MathSciNet  MATH  Google Scholar 

  • Doob J.L., 1953, Stochastic Processes. New York. Tonh Wiley & Sons. 654.

    MATH  Google Scholar 

  • Chen H.F., Guo L., 1985, Adaptive control with recursive identification for stochastic linear systems. Advances in Control and Dynamic Systems, 24.

    Google Scholar 

  • Chen H.F., Guo L., 1986, Convergence rate of least-squares stostochastic systems. Int. Journal of Control, 44, No 5, 1459–1477.

    Article  MATH  Google Scholar 

  • Goodwin G.C., Ramandge P.J., Caines P.E., 1981, Discrete time stochastic adaptive control. SIAM J. Contr. Optimiz., 19, 829–853.

    Article  MATH  Google Scholar 

  • Granichin O.N., Fomin V.N., 1986, Adaptive control using test signals in the feedback channel. Automat. Remote Control, 47, No.2, part 2, 238–248.

    MathSciNet  MATH  Google Scholar 

  • Granichin O.N., 1989, A stochastic recursive procedure with dependent noises in the observation that uses sample perturbations in the Input. Vestnik Leningrad Univ. Math., v.22, No.l, 27–31.

    MathSciNet  MATH  Google Scholar 

  • Granichin O.N., 1990, Construction of a suboptimal controller of a linear object with limited noise. Automat. Remote Control, 51, No.2, part 1, 184–187.

    MathSciNet  MATH  Google Scholar 

  • Granichin O.N., 1992a, Stochastic approximation with sample perturbations in the input. Automat. Remote Control, 53, No. 2, 100–110.

    MathSciNet  Google Scholar 

  • Granichin O.N., 1992b, Unknown function minimum point estimation under dependent noise. Problems Inform. Transmission, 28, No. 2, 90–99.

    MathSciNet  Google Scholar 

  • Lai T.L., Wei C.-Z., 1986, Extended least squares and their applications to adaptive control and prediction in linear systems. IEEE Trans, on Automatic Control, AC-31, No. 10, 899–907.

    MathSciNet  Google Scholar 

  • Ljung L., 1977, Analysis of recursive stochastic algorithms. IEEE Trans. Auto. Control, AC-22, 551–575.

    Article  MathSciNet  MATH  Google Scholar 

  • Katkovnik V.,Ya. Linear Estimates and Stochastic Optimization Problems. Moscow. 1984.

    Google Scholar 

  • Kiefer J., Wolfowitz J., 1952, Statistical estimation on the maximum of a regression function. Ann. Math. Statist, v.23, 462–466.

    Article  MathSciNet  MATH  Google Scholar 

  • Moore J.B., 1978, On strong consistency of least squares identification algorithms. Automatica. 14, 505–509.

    Article  MATH  Google Scholar 

  • Polyak B.T.,1987, Introduction to Optimization. Optim. Software, New York

    Google Scholar 

  • Polyak B.T., Tsybakov A.B., 1990, Optimal orders of accuracy for search algorithms of stochastic optimization. Problems Inform. Transmission, v.26, No.2, 126–133.

    MathSciNet  MATH  Google Scholar 

  • Robbins H., Monro S., 1951, A stochastic approximation method. Ann. Math. Statist, v.22, 400–407.

    Article  MathSciNet  MATH  Google Scholar 

  • Solo V., 1979, The Convergence of AML. IEEE Trans.on Automatic Control, AC-24, 958–962.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media New York

About this chapter

Cite this chapter

Granichin, O.N. (1994). Stochastic Approximation Under Dependent Noises, Detecting Signals and Adaptive Control. In: Anastassiou, G., Rachev, S.T. (eds) Approximation, Probability, and Related Fields. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2494-6_19

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-2494-6_19

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6063-6

  • Online ISBN: 978-1-4615-2494-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics