I.N. Sinitsyn1, V.I. Sinitsyn2, E.R. Korepanov3, T.D. Konashenkova4

1−4 FRC CSC RAS (Moscow, Russia)
 1 sinitsin@dol.ru, 2 vsinitsin@ipiran.ru, 3 ekorepanov@ipiran.ru, 4 tkonashenkova64@mail.ru

Article is devoted to methodological support and software tools for nonlinear stochastic systems with high availability (StSHA) described by Pugachev equation for parameters and additive noises. Noises are independent from parameters. Nonlinear vector methodology is based on Haar wavelet stochastic canonical expansions and Bayes criteria (BC). Basic results:

1) general BC algorithm of StSHA synthesis for inter dependent noises;

2) general BC algorithm of StSHA synthesis for independent noises;

3) two partial algorithms for two criteria: mean square error minimum and damage accumulation special attention is paid to normal parameters of StSHA;

4) software tools "BC-Synthesis-WL.2" in MATLAB;

5) test examples for nonlinear cubic two dimensional StSHA and normal parameters confirming of high accuracy of wavelet oriented algorithms.

Sinitsyn I.N., Sinitsyn V.I., Korepanov E.R., Konashenkova T.D. Software tools for analysis and synthesis of stochastic systems with high availability (XVIII). Highly Available Systems. 2023. V. 19. № 3. P. 18−34. DOI: https://doi.org/ 10.18127/j20729472-202303-02 (in Russian)

1. Sinicyn I.N., Sergeev I.V., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (IV). Sistemy vysokoj dostupnosti. 2017. T. 13. № 3. S. 55–59 (in Russian).
2. Sinicyn I.N., Sergeev I.V., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (V). Sistemy vysokoj dostupnosti. 2018. T. 14. № 1. S. 59–70 (in Russian).
3. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Optimizaciya stohasticheskih sistem na osnove vejvlet kanonicheskih razlozhenij. Avtomatika i telemekhanika. 2020. № 11. S. 138–156 (in Russian).
4. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (XI). Sistemy vysokoj dostupnosti. 2021. T. 17. № 1. S. 25–40. DOI: https://doi.org/10.18127/j20729472-202101-03 (in Russian).
5. Sinitsyn I., Sinitsyn V., Korepanov E., Konashenkova T. Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions. Mathematics. 2022. V. 10. Is. 9. 1517. URL: https://doi.org/10.3390/math10091517.
6. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (XVII). Sistemy vysokoj dostupnosti. 2023. T. 19. № 2. S. 5−24. DOI: https:// doi.org/10.18127/j20729472-202302-01 (in Russian).
7. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Sintez nestacionarnyh sistem metodom vejvlet kanonicheskih razlozhenij. V kn.: Sinicyn I.N. Kanonicheskie predstavleniya sluchajnyh funkcij. Teoriya i primeneniya. M.: TORUS-PRESS. 2023 (in Russian).
8. Sinitsyn I., Sinitsyn V., Korepanov E., Konashenkova T. Synthesis of Nonlinear Nonstationary Stochastic Systems by Wavelet Canonical Expansions. Mathematics. 2023. V. 11. Is. 9. P. 2059. URL: https://doi.org/10.3390/math11092059.
9. Sinicyn I.N. Kanonicheskie predstavleniya sluchajnyh funkcij. Teoriya i primeneniya. M.: TORUS-PRESS. 2023 (in Russian).
10. Proskurin A.V., Sagalakov A.M. Wavelet Approximation and Boundary Eigenvalue Problems in Mathematical Physics. Izvestiya of Altai State University. 2014. № 1. DOI:10.14258/izvasu(2014)1.1-52. URL: https://www.researchgate.net/publication/270526718.
11. Dobeshi I. Desyat' lekcij po vejvletam. Moskva – Izhevsk: NIC «Regulyarnaya i haoticheskaya dinamika». 2004 (in Russian).
12. Pugachev V.S. Teoriya sluchajnyh funkcij i ee primenenie k zadacham avtomaticheskogo upravleniya. Izd. 3-e. M.: Fizmatgiz, 1962.
13. Pugachev V.S., Sinicyn I.N. Teoriya stohasticheskih sistem. M.: Logos. 2000, 2004. [Angl. per. Stochastic Systems Theory and Applications. Singapore. World Scientific, 2001] (in Russian).
14. Boldyrev Yu.Ya. Variacionnoe ischislenie i metody optimizacii: Ucheb. posobie dlya vuzov. M.: Yurajt. 2019 (in Russian).