Nonparametric identification of dynamic systems under normal operation

The research gives nonparametric identification algorithms under the conditions of incomplete a priory information. The identification case differs from the previously known ones due to the fact that, besides the control action, an uncontrollable variable, but a measurable one, impacts on the object input. In contrast to parametric identification, the research considers the situation when the equations describing dynamic objects are not given with accuracy to the parameters. In this case, there are some features to study while getting the recovery characteristics of various object channels. The main characteristic is that the transition response of a channel is taken when the other channel is in a stable position. Moreover, the identification problem is analyzed under normal object operation, opposite to the previously known nonparametric approach based on Heaviside function input to the object and further Duhamel integral application. An arbitrary signal is input to the object during normal operation as a result we have a corresponding response of the object output. It should be noted that the measurements of the input and output variables are carried out with random noise. 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 discrete 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 with the Duhamel integral, we obtain a nonparametric model of a linear dynamical system of unknown order. The article also describes the case of constructing nonparametric model when a delta-shaped function is input to the object. It is interesting to find out how delta-shaped function might differ from the delta function. The weight function is determined in the class of nonparametric Nadaraya-Watson estimates. Previously proposed nonparametric algorithms consider the case when Heaviside function is applied to the object; this narrows the scope of nonparametric identification practical use. It is important to construct nonparametric model of the dynamic object under conditions of normal operation.