Systems and Means of Informatics

2026, Volume 36, Issue 3, pp 128-149

WAVELET NEURAL NETWORK SYNTHESIS OF BILINEAR STOCHASTIC SYSTEM

I. N. Sinitsyn
V. I. Sinitsyn
E. R. Korepanov
T. D. Konashenkova

Abstract

The paper is devoted to methodological and algorithmical support of wavelet neural network (WNN) mean square estimation (MSE) synthesis for an observable bilinear stochastic system (BLStS). The BLStS is described by the Pugachev equations for the input and output stochastic processes (StP). The output StP is dependent on the random parameters vector. The input StP contains random noise independent of random parameters. The random parameters vector is defined by a probability density function. The linear operator for MSE optimal StS is the approximate solution of the operator equation connecting probability second-order moments. The approximate solution is based on the theory of multiscale analysis and a WNN. The random noise is approximated by a wavelet canonical expansion (WLCE) built upon an orthonormal basis of wavelets with compact carrier. This WLCE is constructed on a WNN and is denoted as CEWNN. Input is approximated by linear combination of basic wavelets with random coefficients. The optimal MSE is composed as a linear combination of basic wavelets with random coefficients. Accuracy estimates for the output StP are provided in terms of probability moments of the first and second order. Experimental software tools "BLStS-Synthesis-WNN" and test examples are developed.

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