On Nonparametric Modelling of Multidimensional Noninertial Systems with Delay

Abstract

We consider the problem of noninertial objects identication under nonparametric uncertainty when a priori information about the parametric structure of the object is not available. In many applications there is a situation, when measurements of various output variables are made through signicant period of time and it can substantially exceed the time constant of the object. In this context, we must consider the object as the noninertial with delay. In fact, there are two basic approaches to solve problems of identication: one of them is identication in "narrow" sense or parametric identication. However, it is natural to apply the local approximation methods when we do not have enough a priori information to select the parameter structure. These methods deal with qualitative properties of the object. If the source data of the object is suciently representative, the nonparametric identication gives a satisfactory result but if there are "sparsity" or "gaps" in the space of input and output variables the quality of nonparametric models is signicantly reduced. This article is devoted to the method of lling or generation of training samples based on current available information. This can signicantly improve the accuracy of identication of nonparametric models of noninertial systems with delay. Conducted computing experiments have conrmed that the quality of nonparametric models of noninertial systems can be signicantly improved as a result of original sample "repair". At the same time it helps to increase the accuracy of the model at the border areas of the process input-output variables denition