BULLETIN of the

POLISH ACADEMY of SCIENCES

TECHNICAL SCIENCES

 BULLETIN of the POLISH ACADEMY of SCIENCES: TECHNICAL SCIENCES
Volume 56, Issue 4, December 2008

Electronics
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pp 347 - 359

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Applicational possibilities of nonparametric estimation of distribution density for control engineering

P. KULCZYCKI
Together with the dynamic development of modern computer systems, the possibilities of applying refined methods of nonparametric estimation to control engineering tasks have grown just as fast. This broad and complex theme is presented in this paper for the case of estimation of density of a random variable distribution. Nonparametric methods allow here the useful characterization of probability distributions without arbitrary assumptions regarding their membership to a fixed class. Following an illustratory description of the fundamental procedures used to this end, results will be generalized and synthetically presented of research on the application of kernel estimators, dominant here, in problems of Bayes parameter estimation with asymmetrical polynomial loss function, as well as for fault detection in dynamical systems as objects of automatic control, in the scope of detection, diagnosis and prognosis of malfunctions. To this aim the basics of data analysis and exploration tasks - recognition of outliers, clustering and classification - solved using uniform mathematical apparatus based on the kernel estimators methodology were also investigated.
  
Key words: 

control engineering, nonparametric estimation, density of probability distribution, kernel estimators, data analysis and exploration, Bayes parameter estimation, fault detection, optimal control, robust control.

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Copyright ® Bulletin of the Polish Academy of Sciences: Technical Sciences

December 2008