Systems and Means of Informatics
2026, Volume 36, Issue 2, pp 18-39
WAVELET-NEURAL NETWORK SYNTHESIS OF THE OPTIMAL OBSERVED LINEAR STOCHASTIC PUGACHEV SYSTEM WITH PARAMETRIC NOISES USING THE MEAN-SQUARE CRITERION
- I. N. Sinitsyn
- V. I. Sinitsyn
- E. R. Korepanov
- T. D. Konashenkova
Abstract
Methodological and algorithmical support for wavelet neural network (WNN) synthesis for observable linear scalar Pugachev stochastic system (StS) with parametric noises (PN) and mean square error (MSE) criterion is presented.
Input of StS with PN contains useful signal scalar stochastic process (StP) depending upon random vector parameters and PN. Output StP is fixed. Linear operator MSE-optimal StS is derived by approximate solution of operator equation connecting second probability moments of input and needed output using methods of multiscale analysis (MSA) and WNN. Input StP is presented in the form of linear combination of input random variables (RV) by means of wavelet canonical expansions (WLCE). Mean-square optimal estimate of an output StP is also constructed in the form of linear combination of input RV with coefficients defined by operator equation solution. Formulae based on the first and second probability moments for accuracy of MSE estimate are given. Computer experiments confirm advantages of WNN synthesis based on MSA, WLCE, and WNN in comparison with recurrent synthesis based on MSA and WLCE.
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[+] About this article
Title
WAVELET-NEURAL NETWORK SYNTHESIS OF THE OPTIMAL OBSERVED LINEAR STOCHASTIC PUGACHEV SYSTEM WITH PARAMETRIC NOISES USING THE MEAN-SQUARE CRITERION
Journal
Systems and Means of Informatics
Volume 36, Issue 2, pp 18-39
Cover Date
2026-06-05
DOI
10.14357/08696527260202
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
canonical expansion; mean-square criterion; modeling; optimal estimate; parametric noise; stochastic process; stochastic system; wavelet; wavelet-neural network
Authors
I. N. Sinitsyn  , V. I. Sinitsyn , E. R. Korepanov , and T. D. Konashenkova
Author Affiliations
Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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