Journal of Optimization Theory and Applications

, Volume 68, Issue 2, pp 379–383 | Cite as

Adaptive control of continuous-time linear stochastic systems with discounted cost criterion

  • T. R. Bielecki
Technical Note
  • 54 Downloads

Abstract

In this note, we consider the adaptive control of a linear diffusion process with regard to the discounted cost criterion. We show that the certainty-equivalence type of control, analogous to the one considered by Duncan and Pasik-Duncan (Ref. 1), is asymptotically discount optimal in the sense of Schäl (Ref. 2).

Key Words

Adaptive control discounted cost asymptotically discount optimal control 

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References

  1. 1.
    Duncan, T. E., andPasik-Duncan, B.,Adaptive Control of Continuous-Time Linear Stochastic Systems, Mathematics for Control, Signals, and Systems, Vol. 3, pp. 45–60, 1990.Google Scholar
  2. 2.
    Schäl, M.,Estimation and Control in Discounted Stochastic Dynamic Programming, Stochastics, Vol. 20, pp. 51–71, 1987.Google Scholar
  3. 3.
    Wonham, M.,Linear Multivariable Control: A Geometric Approach, Springer-Verlag, New York, New York, 1979.Google Scholar
  4. 4.
    Duncan, T. E., Goldys, B., andPasik-Duncan, B.,Adaptive Control of Linear Stochastic Evolution Systems, Preprint, Department of Mathematics, University of Kansas.Google Scholar
  5. 5.
    Lipster, R. S., andShiryaev, A. N.,Statistics of Random Processes, I, Springer-Verlag, New York, New York, 1978.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • T. R. Bielecki
    • 1
  1. 1.Department of MathematicsUniversity of KansasLawrence

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