STATIONARY FULLY PROBABILISTIC CONTROL DESIGN

Tatiana V. Guy, Miroslav Kárný

2005

Abstract

Stochastic control design chooses the controller that makes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design describes both the closed-loop and its desired behavior in probabilistic terms and uses the Kullback-Leibler divergence as their proximity measure. Such a design provides explicit minimizer, which opens a way for a simpler approximations of analytically infeasible cases. The current formulations are oriented towards finite-horizon design. Consequently, the optimal strategy is non-stationary one. This paper provides infinite-horizon problem formulation and solution. It leads to a stationary strategy whose approximation is much easier.

References

  1. Berger, J. (1985). Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York.
  2. Haykin, S. (1994). Neural networks: A comprehensive foundation. Macmillan College Publishing Company, New York.
  3. KárnÉ, M. (1996). Towards fully probabilistic control design. Automatica, 32(12):1719-1722.
  4. KárnÉ, M., Böhm, J., Guy, T., Jirsa, L., Nagy, I., Nedoma, P., and Tesar?, L. (2005). Optimized Bayesian Dynamic Advising: Theory and Algorithms. Springer, London. to appear.
  5. KárnÉ, M., Böhm, J., Guy, T. V., and Nedoma, P. (2003). Mixture-based adaptive probabilistic control. International Journal of Adaptive Control and Signal Processing, 17(2):119-132.
  6. KárnÉ, M. and Guy, T. (2004). Fully probabilistic control design. Systems & Control Letters. submitted.
  7. Kullback, S. and Leibler, R. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22:79- 87.
  8. Kushner, H. (1971). Introduction to stochastic control. Holt, Rinehart and Winston, New York, San Francisco, London.
  9. Lee, J.M. and Lee, J.H. (2004). Approximate dynamic procgramming strategies and their applica bility for process control: A review and future directions. International Journal of Control, 2(3):263-278.
  10. Meditch, J. (1969). Stochastic Optimal Linear Estimation and Control. Mc. Graw Hill.
  11. Murray-Smith, R. and Johansen, T. (1997). Multiple Model Approaches to Modelling and Control. Taylor & Francis, London.
  12. Peterka, V. (1981). Bayesian system identification. In Eykhoff, P., editor, Trends and Progress in System Identification, pages 239-304. Pergamon Press, Oxford.
  13. Rabitz, H. and Alis, O. (1999). General foundations of highdimensional model representations. Journal of Mathematical Chemistry, 25:197-233.
  14. Titterington, D., Smith, A., and Makov, U. (1985). Statistical Analysis of Finite Mixtures. John Wiley & Sons, Chichester, New York, Brisbane, Toronto, Singapore. ISBN 0 471 90763 4.
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Paper Citation


in Harvard Style

V. Guy T. and Kárný M. (2005). STATIONARY FULLY PROBABILISTIC CONTROL DESIGN . In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 972-8865-29-5, pages 109-112. DOI: 10.5220/0001183101090112


in Bibtex Style

@conference{icinco05,
author={Tatiana V. Guy and Miroslav Kárný},
title={STATIONARY FULLY PROBABILISTIC CONTROL DESIGN},
booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2005},
pages={109-112},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001183101090112},
isbn={972-8865-29-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - STATIONARY FULLY PROBABILISTIC CONTROL DESIGN
SN - 972-8865-29-5
AU - V. Guy T.
AU - Kárný M.
PY - 2005
SP - 109
EP - 112
DO - 10.5220/0001183101090112