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Title: Estimation of hidden Markov models for a partially observed risk sensitive control problem (English)
Author: Frankpitt, Bernard
Author: Baras, John S.
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 34
Issue: 6
Year: 1998
Pages: [739]-746
Summary lang: English
Category: math
Summary: This paper provides a summary of our recent work on the problem of combined estimation and control of systems described by finite state, hidden Markov models. We establish the stochastic framework for the problem, formulate a separated control policy with risk-sensitive cost functional, describe an estimation scheme for the parameters of the hidden Markov model that describes the plant, and finally indicate how the combined estimation and control problem can be re-formulated in a framework that permits an application of stochastic approximation techniques to the proof of asymptotic convergence of the estimator. (English)
Keyword: hidden Markov model
Keyword: estimation and control problem
Keyword: risk sensitive control problem
Keyword: stochastic approximation techniques
Keyword: asymptotic convergence
MSC: 91B30
MSC: 93E10
MSC: 93E20
idZBL: Zbl 1274.93254
idMR: MR1695375
Date available: 2009-09-24T19:22:17Z
Last updated: 2015-03-28
Stable URL:
Reference: [1] Arapostathis A., Marcus S. I.: Analysis of an identification algorithm arising in the adaptive estimation of Markov chains.Mathematics of Control, Signals and Systems 3 (1990),1–29 Zbl 0685.93063, MR 1027318, 10.1007/BF02551353
Reference: [2] Baras J. S., James M. R.: Robust and Risk–Sensitive Output Feedback Control for Finite State Machines and Hidden Markov Models, to be publishe.
Reference: [3] Benveniste A., Métivier M., Priouret P.: Adaptive Algorithms and Stochastic Approximations.Springer–Verlag, Berlin 1990. Translation of “Algorithmes adaptatifs et approximations stochastiques”, Masson, Paris 1987 Zbl 0752.93073, MR 1082341
Reference: [4] Fernandéz–Gaucherand E., Marcus S. I.: Risk–Sensitive Optimal Control of Hidden Markov Models: Structural Results.Technical Report TR 96-79, Institute for Systems Research, University of Maryland, College Park, Maryland 1996 Zbl 0891.93087
Reference: [5] Fernandéz–Gaucherand E., Arapostathis A., Marcus S. I.: Analysis of an adaptive control scheme for a partially observed controlled Markov chain.IEEE Trans. Automat. Control 38 (1993), 6, 987–993 Zbl 0786.93089, MR 1227213, 10.1109/9.222316
Reference: [6] Krishnamurthy, V, Moore J. B.: On–line estimation of hidden Markov model parameters based on the.IEEE Trans. Signal Processing 41 (1993), 8, 2557–2573 Zbl 0825.93742
Reference: [7] Gland F. Le, Mevel L.: Geometric Ergodicity in Hidden Markov Models.Technical Report No. 1028, IRISA/INRIA, Campus de Beaulieu, Renees 1996 Zbl 0941.93053


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