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Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions

Author

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  • Igor Sinitsyn

    (Federal Research Center “Computer Science and Control”, Russian Academy of Sciences (FRC CSC RAS), 119333 Moscow, Russia
    Moscow Aviation Institute, National Research University, 125993 Moscow, Russia)

  • Vladimir Sinitsyn

    (Federal Research Center “Computer Science and Control”, Russian Academy of Sciences (FRC CSC RAS), 119333 Moscow, Russia
    Moscow Aviation Institute, National Research University, 125993 Moscow, Russia)

  • Eduard Korepanov

    (Federal Research Center “Computer Science and Control”, Russian Academy of Sciences (FRC CSC RAS), 119333 Moscow, Russia)

  • Tatyana Konashenkova

    (Federal Research Center “Computer Science and Control”, Russian Academy of Sciences (FRC CSC RAS), 119333 Moscow, Russia)

Abstract

This article is devoted to analysis and optimization problems of stochastic systems based on wavelet canonical expansions. Basic new results: (i) for general Bayes criteria, a method of synthesized methodological support and a software tool for nonstationary normal (Gaussian) linear observable stochastic systems by Haar wavelet canonical expansions are presented; (ii) a method of synthesis of a linear optimal observable system for criterion of the maximal probability that a signal will not exceed a particular value in absolute magnitude is given. Applications: wavelet model building of essentially nonstationary stochastic processes and parameters calibration.

Suggested Citation

  • Igor Sinitsyn & Vladimir Sinitsyn & Eduard Korepanov & Tatyana Konashenkova, 2022. "Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions," Mathematics, MDPI, vol. 10(9), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1517-:d:807379
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    References listed on IDEAS

    as
    1. Lepik, Ü., 2005. "Numerical solution of differential equations using Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(2), pages 127-143.
    2. Hsiao, Chun-Hui, 1997. "State analysis of linear time delayed systems via Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(5), pages 457-470.
    3. Igor Sinitsyn & Vladimir Sinitsyn & Eduard Korepanov & Tatyana Konashenkova, 2021. "Wavelet Modeling of Control Stochastic Systems at Complex Shock Disturbances," Mathematics, MDPI, vol. 9(20), pages 1-15, October.
    4. Hsiao, C.H., 2004. "Haar wavelet approach to linear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 561-567.
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    Cited by:

    1. Natalia Bakhtadze, 2023. "Preface to the Special Issue on “Identification, Knowledge Engineering and Digital Modeling for Adaptive and Intelligent Control”—Special Issue Book," Mathematics, MDPI, vol. 11(8), pages 1-3, April.
    2. Igor Sinitsyn & Vladimir Sinitsyn & Eduard Korepanov & Tatyana Konashenkova, 2023. "Synthesis of Nonlinear Nonstationary Stochastic Systems by Wavelet Canonical Expansions," Mathematics, MDPI, vol. 11(9), pages 1-18, April.

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