Identification of Dynamic Objects using a Family of Experimental Supporting Integral Curves

Abstract

A specially planned experiment based on obtaining a required family of estimates of supporting integral curves (approximately described in a given finite system of base functions) is used to solve a problem of active identification of a dynamic object, which corresponds to an a priori unknown differential equation. In view of the fact that experimental data may contain fluctuation and singular interference, a method is developed for optimal unbiased estimation of linear quantitative characteristics of the object behavior and an approximate analytical solution (differential equation), which is valid for a given set of permitted time values and an initial condition. The basic characteristics of the method are substantiated, and the results of the computational experiment are presented.