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Analysis of an adaptive control scheme for a partially observed controlled Markov chain

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3 Author(s)
Fernandez-Gaucherand, E. ; Dept. of Syst. & Ind. Eng., Arizona Univ., Tucson, AZ, USA ; Arapostathis, A. ; Marcus, S.I.

The authors consider an adaptive finite state controlled Markov chain with partial state information, motivated by a class of replacement problems. They present parameter estimation techniques based on the information available after actions that reset the state to a known value are taken. It is proved that the parameter estimates converge w.p.1 to the true (unknown) parameter, under the feedback structure induced by a certainty equivalent adaptive policy. It is shown that the adaptive policy is self-optimizing in a long-run average sense, for any (measurable) sequence of parameter estimates converging w.p.1 to the true parameter

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Automatic Control, IEEE Transactions on  (Volume:38 ,  Issue: 6 )