Synthesis of Nonlinear Nonstationary Stochastic Systems by Wavelet Canonical Expansions

Igor Sinitsyn, Vladimir Sinitsyn, Eduard Korepanov and Tatyana Konashenkova ()
Additional contact information
Igor Sinitsyn: Federal Research Center “Computer Science and Control”, Russian Academy of Sciences (FRC CSC RAS), 119333 Moscow, Russia
Vladimir Sinitsyn: Federal Research Center “Computer Science and Control”, Russian Academy of Sciences (FRC CSC RAS), 119333 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

Mathematics, 2023, vol. 11, issue 9, 1-18

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.

Keywords: Bayes’ criterion; damage accumulation criterion; Haar wavelets; stochastic process; wavelet canonical expansion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/9/2059/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/9/2059/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:9:p:2059-:d:1133772

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().