
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 2, Pages 267–282
(Mi vuu586)




This article is cited in 1 scientific paper (total in 1 paper)
MATHEMATICS
On using Gaussian functions with varied parameters for approximation of functions of one variable on a finite segment
A. V. Chernov^{ab} ^{a} Nizhni Novgorod State University, pr. Gagarina, 23,
Nizhni Novgorod, 603950, Russia
^{b} Nizhni Novgorod State Technical University, ul. Minina, 24,
Nizhni Novgorod, 603950, Russia
Abstract:
We study the opportunities of approximation of a piecewise continuous function on a finite segment by a linear combination of $\mu$ Gaussian functions, with the object of their usage for control approximation in lumped problems of optimal control. Recall that a Gaussian function (quadratic exponent) is one defined as follows $\varphi(x)=\dfrac{1}{\sigma\sqrt{2\pi}} \exp[ \dfrac{(xm)^2}{2\sigma^2} ]$. Unlike investigations carried out by another authors, we consider the case where the parameters of a Gaussian function (with the coefficients of a linear combination) are varied and selected, in particular, by minimization of the difference between a function being approximated and its approximation, or (in the case of an optimal control problem) by minimization of the cost functional. Such an approach gives the opportunity to approximate optimal control problems with lumped parameters by finite dimensional problems of mathematical programming of comparatively small dimension (as opposed to piecewise constant or piecewise linear approximation on a fixed mesh with small width which is usually used). We present also some results of numerical experiments which substantiate efficiency of the approach under study.
Keywords:
control parametrization technique, lumped problem of optimal control, approximation by quadratic exponents, Gaussian function.
DOI:
https://doi.org/10.20537/vm170210
Full text:
PDF file (336 kB)
References:
PDF file
HTML file
Bibliographic databases:
UDC:
517.518
MSC: 41A30 Received: 05.03.2017
Citation:
A. V. Chernov, “On using Gaussian functions with varied parameters for approximation of functions of one variable on a finite segment”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:2 (2017), 267–282
Citation in format AMSBIB
\Bibitem{Che17}
\by A.~V.~Chernov
\paper On using Gaussian functions with varied parameters for approximation of functions of one variable on a finite segment
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 2
\pages 267282
\mathnet{http://mi.mathnet.ru/vuu586}
\crossref{https://doi.org/10.20537/vm170210}
\elib{http://elibrary.ru/item.asp?id=29410198}
Linking options:
http://mi.mathnet.ru/eng/vuu586 http://mi.mathnet.ru/eng/vuu/v27/i2/p267
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:

A. V. Chernov, “O primenenii kvadratichnykh eksponent dlya diskretizatsii zadach optimalnogo upravleniya”, Vestn. Udmurtsk. unta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 558–575

Number of views: 
This page:  2108  Full text:  57  References:  25 
