Skip to main content

Some Connections between Statistics and Control Theory

  • Chapter
Mathematical Statistics and Probability Theory

Abstract

Linear controlled systems with a quadratic cost function are dealt with. Using concepts of estimation theory the efficiency of a control is introduced. For systems with unknown parameters estimated by the least squares method the asymptotic distribution of the cost is derived.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Davis, M.H.A. and Vinter, R.B. (1984). Stochastic Modelling and Control. Chapman and Hall, London.

    Google Scholar 

  • Duncan, T.E. and Pasik-Duncan, B. (1985) Adaptive control of continuous time linear systems. Preprint, University of Kansas.

    Google Scholar 

  • Mc. Kean, H.P. (1969). Stochastic Integrals. Academic Press, New York.

    Google Scholar 

  • Kucera, V. (1973). A review of the matrix Riccati equation. Kybernetika (Prague) 9, 42–61.

    MathSciNet  MATH  Google Scholar 

  • Kumar, P.R. (1985) A survey of some results in stochastic adaptive control. SIAM J. Control and Optimization 23, 329–380.

    Google Scholar 

  • Kurano, M. (1972). Discrete-time Markovian decision processes with an unknown parameter:average return criterion. J. Op. Research Soc. Japan 15, 67–76.

    MathSciNet  MATH  Google Scholar 

  • Mandl, P. (1972). An application of Itô’s formula to stochastic control systems. In Lecture Notes in Mathematics 294 Springer-Verlag, Berlin, 8–13.

    Google Scholar 

  • Mandl, P. (1986). Asymptotic ordering of probability distributions for linear controlled systems with quadratic cost. In Lecture Notes in Control and Inf. Sc. 78, Springer-Verlag, Berlin, 277–283.

    Google Scholar 

  • Mandl, P. (1987a). Limit theorems of probability theory and optimality in linear controlled systems with quadratic cost. In Proc. of 5th IFIP Working Conference on Stochastic Differential Systems. To appear.

    Google Scholar 

  • Mandl, P. (1987b). On transient phenomena in self-optimizing control systems. In Trans, of 10th Prague Conference on Information Theory etc. To appear.

    Google Scholar 

  • Pasik-Duncan, B. (1985) On adaptive control. Preprint. Central School of Planning and Statistics, Warsaw.

    Google Scholar 

  • Schäl, M. (198U) Asymptotic results for sequential Markov decision models under uncertainty. Statistics and Decisions 2, 39–62.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 by D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Mandl, P. (1987). Some Connections between Statistics and Control Theory. In: Bauer, P., Konecny, F., Wertz, W. (eds) Mathematical Statistics and Probability Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3965-3_15

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3965-3_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8259-4

  • Online ISBN: 978-94-009-3965-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics