Terminal Invariance of Stochastic Diffusion Systems

For a controlled stochastic diffusion system, we obtain sufficient conditions for the terminal criterion to be constant with probability one on the assumption of fixed initial state (invariance in perturbations) and sufficient conditions for the terminal criterion to be independent with probability one both from the realization of the random process and the initial conditions (absolute invariance).

Keywords

Stochastic systems, weak invariance, absolute invariance, control

Received

30.09.2018

Publication date

30.09.2018

Number of characters

427

Cite Download pdf To download PDF you should sign in

GOST	Khrustalev M. Terminal Invariance of Stochastic Diffusion Systems // Avtomatika i Telemekhanika – 2018. – Issue 8 C. 81-100 [Electronic resource]. URL: http://ras.jes.su/ait/s207987840000496-4-1-en (circulation date: 01.12.2023). DOI: 10.31857/S000523100001249-7
MLA	Khrustalev, Michael "Terminal Invariance of Stochastic Diffusion Systems." Avtomatika i Telemekhanika 8 (2018):81-100. DOI: 10.31857/S000523100001249-7
APA	Khrustalev M. (2018). Terminal Invariance of Stochastic Diffusion Systems. Avtomatika i Telemekhanika (8), pp.81-100 DOI: 10.31857/S000523100001249-7

Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

Readers community rating: votes 0

1. Rozonoer L.I. A Variational Approach to the Problem of Invariance of Automation Control Systems // Autom. Remote Control. 1963. V. 24. No. 6. P. 680–743; 1963. V. 24. No. 7. P. 793–800.

2. Khrustalev M.M. Necessary and Sufficient Conditions of Invariance // Autom. Remote Control. 1968. V. 29. No. 4. P. 540–544.

3. Khrustalev M.M. Metody teorii invariantnosti v zadachakh sinteza zakonov terminal'nogo upravleniya letatel'nymi apparatami. Uch. pos. M: MAI, 1987.

4. Schipanov G.V. Teoriya i metody proektirovaniya avtomaticheskikh regulyatorov // AiT. 1939. № 1. S. 49–66.

5. Luzin N.N. K izucheniyu matrichnoj teorii differentsial'nykh uravnenij // AiT. 1940. № 5. S. 3–66.

6. Pushkarev Y.A., Rodygin V.A. A Terminal Invariance Criterion in Deterministic Motion Control Systems // J. Comput. Syst. Sci. Int. 2011. V. 50. No. 4. P. 544–554.

7. Batenko A.P. Sistemy terminal'nogo upravleniya. M.: Radio i svyaz', 1984.

8. Legen'kij V.I. O postroenii sistem upravleniya s invariantnoj programmoj // Matematicheskie mashiny i sistemy. 2004. № 1. S. 115–121.

9. Petrov B.N., Portnov-Sokolov Yu.P., Andrienko A.Ya., Ivanov V.P. Bortovye terminal'nye sistemy upravleniya. Printsipy postroeniya i ehlementy teorii. M.: Mashinostroenie, 1983.

10. Zhevnin A.A. Printsipy postroeniya sistem terminal'nogo upravleniya ne statsionarnymi linejnymi ob'ektamina osnove obratnojzadachi dinamiki // Analiticheskie metody sinteza regulyatorov. Mezhvuz. nauch. sb. Saratov: Izd-vo Saratov. politekhn. in-ta, 1978. S. 89–99.

11. Bek V.V., Vishnyakov Yu.S., Makhlin A.R. Integrirovannye sistemy terminal'nogo upravleniya. M.: Nauka, 1989.

12. Bodner V.A., Rodnischev N.E., Yurikov E.P. Optimizatsiya terminal'nykh stokhasticheskikh sistem. M.: Mashinostroenie, 1987.

13. Dubko V.A. Voprosy teorii i primeneniya stokhasticheskikh differentsial'nykh uravnenij. Vladivostok: DVO AN SSSR, 1989.

14. Karachanskaya E.V. Postroenie mnozhestva differentsial'nykh uravnenij s zadannym naborom pervykh integralov // Vestn. TOGU. 2011. № 3 (22). S. 47–56.

15. Aleksandrova O.V. Simmetriya i pervye integraly sistem stokhasticheskikh differentsial'nykh uravnenij Ito // Vestn. Novgorod. gos. un-ta. 2013. T. 1. № 75. S. 54–59.

16. Khrustalev M.M. Slabaya invariantnost' stokhasticheskikh sistem diffuzionnogo tipa // Tr. XI Mezhdunar. Chetaevskoj konf. Analiticheskaya mekhanika, ustojchivost' i upravlenie. T. 3. Ch. III. Kazan': KNITU-KAI, 2017. S. 171–177.

17. Khrustalev M.M. Invariance of Stochastic Diffusion Systems // Doklady Mathematics. 2017. V. 96. No. 2. P. 535–537.

18. Korolyuk V.S., Portenko N.I., Skorokhod A.V., Turbin A.F. Spravochnik po teorii veroyatnostej i matematicheskoj statistike. M.: Nauka, 1985.

19. Khrustalev M.M., Plotnikov Ju.P., Belov V.A. The Invariant Control of Vehicle Descent into the Atmosphere // Acta Astronautica. 1976. No. 5–6. P. 357–367.

20. Kamke Eh. Spravochnik po differentsial'nym uravneniyam v chastnykh proizvodnykh pervogo poryadka. M.: Nauka, 1966.

21. Bulinskij A.V., Shiryaev A.N. Teoriya sluchajnykh protsessov. M.: Fizmatlit, 2005.

22. Mil'shtejn G.N. Chislennoe integrirovanie stokhasticheskikh differentsial'nykh uravnenij. Sverdlovsk: Izd-vo Ural. un-ta, 1988.

23. Paraev Yu.I. Vvedenie v statisticheskuyu dinamiku protsessov upravleniya i fil'tratsii. M.: Sov. radio, 1976.