Piotr Kulczycki, Małgorzata Charytanowicz Asymmetrical Conditional Bayes Parameter Identification for Control Engineering Cybernetics and Systems, vol. 39, no. 3, pp. 229-243, 2008
Abstract:
One of the main problems in control engineering practice results from unavoidable errors in specifying parameters existing in the object model and the necessity to deal with the unwanted phenomena arising as a result. In this paper a Bayes methodology considering both asymmetrical and conditional aspects is applied for this purpose, with the application of kernel estimators methodology. Use of the Bayes rule enables minimum potential losses to be assumed, while the asymmetry of the occurring loss function also enables the inclusion of different results for under- and overestimation. A conditional approach allows to obtain a more precise result thanks to using information entered as the fixed (e.g. current) values of conditioning factors of continuous and/or binary (also categorical) type. The nonparametric methodology of statistical kernel estimators frees the procedure from arbitrary assumptions concerning the forms of distributions characterizing both the parameter under investigation and conditioning factors. The generalizations introduced here also allow different relevance of particular random sample elements to be taken into account.
Key words:
parameter identification, control engineering, Bayes methodology, asymmetrical loss function, conditional factors, statistical kernel estimators.