To nonparametric identification of dynamic systems under normal operation

The problem of nonparametric identification of linear dynamic objects is being investigated. In contrast with para- metric identification, the case is analyzed when equations describing a dynamic object are not specified according to the parameters. Moreover, the identification problem is analyzed under normal object operation, opposite to the previ- ously known nonparametric approach based on Heaviside function input to the object and further Duhamel integral application. An arbitrary signal is inputted to the object during normal operation and weight function realizations are represented by observations of input-output object variables measured with random interferences. As a result, we have a sample of input-output variables. As linear dynamical system can be described by the Duhamel integral, with known input and output object variables, corresponding values of the weight function can be found. This is achieved by dis- crete representation of the latter. Having such realization, nonparametric estimate of the weight function in the form of the nonparametric Nadaraya-Watson estimate is used later. Substituting this into the Duhamel integral, we obtain a nonparametric model of a linear dynamical system of unknown order. The article also describes the case of nonparametric model constructing when a delta-shaped function is inputted to the object. It was interesting to find out how delta-shaped function might differ from the delta function. The weight function was determined in the class of nonparametric Nadaraya-Watson estimates. Nonparametric models were investigated by means of statistical modeling. In general, nonparametric models have shown sufficient efficiency in terms of accuracy prediction by nonparametric model in relation to the actually measured output of the object. Evi- dentally, the accuracy of nonparametric models reduces with the growing influence of interference from the meas- urement of input-output variables or the discreteness of their measurement. Previously proposed nonparametric al- gorithms consider the case when Heaviside function was applied to the object, which narrows the scope of nonpara- metric identification practical use. It is important to construct nonparametric model of a dynamic object in condi- tions of normal operation.