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Adaptive control of Markov chains

  • Vivek Borkar
  • Pravin Varaiya
Part II: Research Reports
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 16)

Abstract

Consider a controlled Markov chain whose transition probabilities are parameterized by α known to be in a finite set A. To each α is associated a prespecified control law φ(α). The adaptive controller selects at each time t the control action indicated by φ(αt), where αt is the maximum likelihood estimate of α. The asymptotic behavior of αt is studied.

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References

  1. [1]
    M.H. Degroot, Optimal Statistical Decisions, McGraw-Hill, New York, 1970.Google Scholar
  2. [2]
    Y. Bar-Shalom and E. Tse, Dual effect, certainty equivalence, and separation in stochastic control, IEEE Trans. Aut. Cont. AC-19(5), 494–500, 1974.Google Scholar
  3. [3]
    P. Mandl, Estimation and control in Markov chains, Adv. Appl. Prob. 6, 40–60, 1974.Google Scholar
  4. [4]
    K.J. Astrom and B. Wittenmark, On self-tuning regulators, Automatica 9, 185–199, 1973.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Vivek Borkar
    • 1
  • Pravin Varaiya
    • 1
  1. 1.Departement of Electrical Engineering and Computer Sciences and the Electronics Research LaboratoryUniversity of CaliforniaBerkeley

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