Estimation of hidden Markov models for a partially observed risk sensitive control problem

Bernard Frankpitt; John S. Baras

Kybernetika (1998)

  • Volume: 34, Issue: 6, page [739]-746
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Frankpitt, Bernard, and Baras, John S.. "Estimation of hidden Markov models for a partially observed risk sensitive control problem." Kybernetika 34.6 (1998): [739]-746. <http://eudml.org/doc/33402>.

@article{Frankpitt1998,
abstract = {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.},
author = {Frankpitt, Bernard, Baras, John S.},
journal = {Kybernetika},
keywords = {hidden Markov model; estimation and control problem; risk sensitive control problem; stochastic approximation techniques; asymptotic convergence; hidden Markov model; estimation and control problem; risk sensitive control problem; stochastic approximation techniques; asymptotic convergence},
language = {eng},
number = {6},
pages = {[739]-746},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Estimation of hidden Markov models for a partially observed risk sensitive control problem},
url = {http://eudml.org/doc/33402},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Frankpitt, Bernard
AU - Baras, John S.
TI - Estimation of hidden Markov models for a partially observed risk sensitive control problem
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 6
SP - [739]
EP - 746
AB - 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.
LA - eng
KW - hidden Markov model; estimation and control problem; risk sensitive control problem; stochastic approximation techniques; asymptotic convergence; hidden Markov model; estimation and control problem; risk sensitive control problem; stochastic approximation techniques; asymptotic convergence
UR - http://eudml.org/doc/33402
ER -

References

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  1. Arapostathis A., Marcus S. I., 10.1007/BF02551353, Mathematics of Control, Signals and Systems 3 (1990),1–29 (1990) Zbl0685.93063MR1027318DOI10.1007/BF02551353
  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 
  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 (1990) Zbl0752.93073MR1082341
  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 Zbl0891.93087
  5. Fernandéz–Gaucherand E., Arapostathis A., Marcus S. I., 10.1109/9.222316, IEEE Trans. Automat. Control 38 (1993), 6, 987–993 (1993) Zbl0786.93089MR1227213DOI10.1109/9.222316
  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 (1993) Zbl0825.93742
  7. Gland F. Le, Mevel L., Geometric Ergodicity in Hidden Markov Models, Technical Report No. 1028, IRISA/INRIA, Campus de Beaulieu, Renees 1996 Zbl0941.93053

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