Dynamic Operator Extraction Method

Abstract

A "black box" is used to mean an object whose internal structure is unknown and information about its structure and functioning can only be partially obtained by analyzing the input-output connections of this object. Not only those material, energy and/or informational flows that are necessary for its functioning in accordance with the goals set before it - signals, but also those that actually complicate the realization of the set goal by the system - obstacles come to the input of the system from the external environment. An unregulated facility is being explored here. When studying such an object, it is important that the signals always describe the behavior of the object as a whole and reflect the individual movements of a large number of its microparticles of the same type. The analysis of the structure of the object based on its established signal is insufficient, if only the dynamic dependence on time is taken into account, even the most detailed registration of the single solution of the established dynamic equation does not allow revealing the structure of the operator in real situations. The inadequacy of the usual black box scheme for studying an unregulated object based on a settled signal leads to the need to account for internal fluctuations in the equations of the object signal. Therefore, the article considers autonomous objects, in the dynamic equations of which time t is not explicitly included. The work formulates and to some extent substantiates a fairly general and fairly simple principle of signal description. According to this basic premise, the properties of the signal, which are quantitatively significant and regularly manifest under the given conditions of observation, are connected to each other by some dynamic structure of the object. The role of object movements, which are less important under these conditions, as well as the role of the external environment, is reflected in this description by the time-fluctuating force  that disturbs the dynamic system. The study of the statistical properties of the response of the dynamic system to the fluctuating disturbance  allows, in a fairly wide range of problems, to evaluate the dynamic characteristics of an unregulated object based on the established signal. The behavior of the signal, which is described by a linearized equation, requires the estimation of the coefficient , so the article considers possible schemes for estimating this coefficient