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2021 | OriginalPaper | Chapter

The Multiplicative-Isolating Principle of Significantly Nonlinear Mathematical Models Creation

Authors : Rudolf Neydorf, Anatoly Gaiduk, Nikita Gamayunov

Published in: Cyber-Physical Systems: Modelling and Intelligent Control

Publisher: Springer International Publishing

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Abstract

A new principle of mathematical models creation for the technical and other objects which are characterized by essential nonlinearity of interdependence of variables is substantiated. It is shown that the use of special analytical functions with a number of unique properties for the multiplicative transformation of fragmented mathematical models that approximate certain parts of the modeled dependencies allows us to obtain new functions that are analytically isolated in their domain of definition. The analyticity of these functions makes it possible additively to combine them into a single analytical function that approximates the simulated dependence in the entire area of its description. In this case, the total approximation error of the mathematical model of the studied object does not exceed the largest error of fragmentary approximating functions. The unique properties of multiplicatively isolating functions provide an almost “seamless” additive union of fragments. This chapter is dedicated to the study and proof of these properties, which are illustrated by examples.

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Title: The Multiplicative-Isolating Principle of Significantly Nonlinear Mathematical Models Creation
Authors: Rudolf Neydorf
Anatoly Gaiduk
Nikita Gamayunov
Publisher: Springer International Publishing
Book: Cyber-Physical Systems: Modelling and Intelligent Control
Print ISBN: 978-3-030-66076-5

Electronic ISBN: 978-3-030-66077-2

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-66077-2_3

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