Systems and Means of Informatics
2024, Volume 34, Issue 3, pp 87-108
NEURAL NETWORK SYNTHESIS OF AN OPTIMAL LINEAR STOCHASTIC SYSTEM ACCORDING TO THE CRITERION OF MINIMUM MEAN SQUARE ERROR
- I. N. Sinitsyn
- V. I. Sinitsyn
- E. R. Korepanov
- T. D. Konashenkova
Abstract
The paper is devoted to the new synthesis method for linear optimal stochastic systems according to the criterion of minimum mean square error (MSE) and neural network technology. It is supposed that one-dimensional input signal is the sum of known signal and additive Gaussian noise. Noise is independent of signal parameters. At output, it is necessary to perform corresponding input transformation. The paper describes architecture of three-layer wavelet neural network (WNN) with one reserved layer. The activation function of reserved layer is described using orthonormal wavelet basis with compact carrier. For WNN functioning, a tutoring algorithm based on the method of quick descend is used.
The MSE optimal operator is constructed. The MSE estimate is presented in the form of linear combination of basis wavelet functions. An illustrative example is given. The basic results are formulated and discussed.
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[+] About this article
Title
NEURAL NETWORK SYNTHESIS OF AN OPTIMAL LINEAR STOCHASTIC SYSTEM ACCORDING TO THE CRITERION OF MINIMUM MEAN SQUARE ERROR
Journal
Systems and Means of Informatics
Volume 34, Issue 3, pp 87-108
Cover Date
2024-10-30
DOI
10.14357/08696527240307
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
canonical expansion; mean square estimate; modeling; optimal estimate; optimal system; 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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