Fernández-Gaucherand, Emmanuel; Arapostathis, Aristotle; Marcus, Steven I. Adaptive control of a partially observed controlled Markov chain. (English) Zbl 0813.93073 Duncan, T. E. (ed.) et al., Stochastic theory and adaptive control. Proceedings of a workshop held at Lawrence, KS (USA), September 26-28, 1991. Berlin: Springer-Verlag. Lect. Notes Control Inf. Sci. 184, 161-171 (1992). The paper deals with the control of a partially observable Markov chain arising in a binary replacement problem with long-run average cost. The transition probabilities of the Markov chain depend on the unknown failure rate of the system. It is shown that the certainty equivalent stochastic policy is self optimizing for any consistent estimator of the unknown parameter. A suitable estimator of this type is also provided.For the entire collection see [Zbl 0778.00021]. Reviewer: G.Di Masi (Padova) MSC: 93E35 Stochastic learning and adaptive control 93E12 Identification in stochastic control theory 93C40 Adaptive control/observation systems 93B07 Observability 93E03 Stochastic systems in control theory (general) 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) Keywords:adaptive control; parameter estimation PDFBibTeX XMLCite \textit{E. Fernández-Gaucherand} et al., Lect. Notes Control Inf. Sci. 184, 161--171 (1992; Zbl 0813.93073)