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Synthesis of Nonlinear Nonstationary Stochastic Systems by Wavelet Canonical Expansions

Author

Listed:
  • 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

The article is devoted to Bayes optimization problems of nonlinear observable stochastic systems (NLOStSs) based on wavelet canonical expansions (WLCEs). Input stochastic processes (StPs) and output StPs of considered nonlinearly StSs depend on random parameters and additive independent Gaussian noises. For stochastic synthesis we use a Bayes approach with the given loss function and minimum risk condition. WLCEs are formed by covariance function expansion coefficients of two-dimensional orthonormal basis of wavelet with a compact carrier. New results: (i) a common Bayes’ criteria synthesis algorithm for NLOStSs by WLCE is presented; (ii) partial synthesis algorithms for three of Bayes’ criteria (minimum mean square error, damage accumulation and probability of error exit outside the limits) are given; (iii) an approximate algorithm based on statistical linearization; (iv) three test examples. Applications: wavelet optimization and parameter calibration in complex measurement and control systems. Some generalizations are formulated.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2059-:d:1133772
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    1. 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.
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