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Adaptive control of Markov chains, I: Finite parameter set

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2 Author(s)
V. Borkar ; University of California, Berkeley, CA, USA ; P. Varaiya

Consider a controlled Markov chain whose transition probabilities depend upon an unknown parameter α taking values in finite set A . To each α is associated a prespecified stationary control law \phi(\alpha ) . The adaptive control law selects at each time t the control action indicated by \phi(\alpha _{t}) where αtis the maximum likelihood estimate of α. It is shown that αtconverges to a parameter α*such that the "closed-loop" transition probabilities corresponding to α*and \phi(\alpha ^{\ast }) are the same as those corresponding to α0and \phi(\alpha ) where α0is the true parameter. The situation when α0does not belong to the model set A is briefly discussed.

Published in:

IEEE Transactions on Automatic Control  (Volume:24 ,  Issue: 6 )