An algorithm for Bayes parameter identification with quadratic asymmetrical loss function

• Autorzy: Kulczycki P. , Mazgaj A.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the estimation problem of model parameter values, in tasks where overestimation implies results other than underestimation, and wliere losses arising from this can be described by a quadratic function with different coefficients characterizing positive and negative errors. In the approach presented, the Bayes decision rule was used, allowing for minimizing potential losses. Calculation algorithms were based on the theory of statistical kernel estimators, which frees the method from distribution type. The result constitutes a complete numerical procedure enabling effective calculation of the value of an identified parameter or - in the multidimensional case - the vector of parameters. The method is aimed at both of the main contemporary approaches to uncertainty modeling: probabilistic and fuzzy logic. It is universal in nature and can be applied in a wide range of tasks of engineering, economy, sociology, biomedicine and other related fields.

Słowa kluczowe

EN

parameter identification; Bayes decision; quadratic asymmetrical loss function; kernel estimators; optimal control

PL

sterowanie optymalne

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2005
• Tom: Vol. 34, no 4
• Strony: 1127--1148
• Opis fizyczny: Bibliogr. 12 poz., wykr.

Twórcy

autor

Kulczycki P.

• Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warszawa, Poland

autor

Mazgaj A.

• Department of Automatic Control Faculty of Electrical and Computer Engineering Cracow University of Technology Warszawska 24, 31-155 Cracow, Poland

Bibliografia

• Athans, M. and Falb, P.L. (1966) Optimal Control. McGraw-Hill, New York.
• Berger, J.O. (1980) Statistical Decision Theory. Springer-Verlag, New York.
• Dahlquist, G. and Bjorck, A. (1983) Numerical Methods. Prentice-Hall, Englewood Clifs.
• Kulczycki, P. (2000) Fuzzy Controller forMechanical Systems. IEEE Transactions on Fuzzy Systems, 8, 5, 645-652.
• Kulczycki, P. (2001) An Algorithm for Bayes Parameter Identification. Journal of Dynamic Systems, Measurement, and Control, 123, 4, 611-614, 2001.
• Kulczycki, P. (2005) Estymatory jądrowe w analizie systemowej. WNT, Warsaw, in press.
• Kulczycki, P. and Mazgaj A. (2003) Parameter Identification with Nonsymmetrical Quadratic Loss Function for Optimal Control. 9th IEEE International Conference on Methods and Models in Automation and Robotics, Międzyzdroje (Poland), 25-28 August 2003, 1, 689-694, CD: I1-5.
• Kulczycki, P. and Wisniewski R. (2002) Fuzzy Controller for a System with Uncertain Load. Fuzzy Sets and Systems, 131, 2, 185-195.
• Mazgaj, A. (2005) Modelowanie niepewności parametrów obiektu dla potrzeb sterowania optymalnego. Ph.D.-thesis, AGH – Cracow University of Science and Technology, Cracow (Poland).
• Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall, New York.
• Stoer, J. and Bulirsch, R. (1983) Introduction to Numerical Analysis. Springer-Verlag, New York.
• Wand, M.P. and Jones, M.C. (1995) Kernel Smoothing. Chapman and Hall, London, 1995.