DOI
10.34229/KCA2522-9664.24.3.13
UDC 519.21
ON THE EXISTENCE OF OPTIMAL CONTROL FOR STOCHASTIC FUNCTIONAL
DIFFERENTIAL EQUATIONS UNDER THE INFLUENCE OF EXTERNAL DISTURBANCES
Abstract. The article discusses the comparison theorem for solutions of stochastic functional differential equations under the influence of external disturbances and its application to one stochastic control problem.
Keywords: comparison theorem, stochastic control, stochastic functional differential equations.
full text
REFERENCES
- Bellman R. Dynamic programming and stochastic control processes. Information and Control. 1958. Vol. 1, Iss. 3. P. 228–239. https://doi.org/10.1016/S0019-9958(58)80003-0.
- Gikhman I.I., Skorokhod A.V. Stochastic differential equations [in Russian]. Kyiv: Nauk. Dumka, 1968. 354 p.
- Gikhman I.I., Skorokhod A.V. Stochastic differential equations and their applications [in Russian]. Kyiv: Nauk. Dumka, 1982. 612 p.
- Kolmanovsky V.B., Shaikhet L.E. On one method for constructing an approximate synthesis of optimal control. Dop AN USSR. Ser .А. 1978. N8. P. 32–36.
- Toshio Yamada. On a comparison theorem for solutions of stochastic differential equations and its applications. Journal Math. Kyoto Univ. 1973. Vol. 13(3). P. 497–512. https://doi.org/10.1215/kjm/1250523 .
- Tokuzo Shiga. Diffusion processes in population genetics. Journal Math. Kyoto Univ. 1981. Vol. 21 (1). P. 133–151.
- Ikeda N., Watanabe S. Stochastic differential equations and diffusion processes. Amsterdam: North-Holland Mathematical Library, 1989. 568 p.
- Knopov P.S. Optimization and identification of stochastic systems. Cybernetics and Systems Analysis. 2023. Vol. 59, N 3. P. 375–384. https://doi.org/10.1007/s10559-023-00572-4.
- Tsarkov E.F., Yasinskyi V.K. Quasilinear stochastic differential equations [in Russian]. Riga: Oriyentir, 1992. 328 p.
- Oksendal B. Stochastic differential equations an introduction with applications. Sixth edition. Heidelberg; New York; Dordrecht; London: Springer Science + Business Media, 2013. https://doi.org/10.1007/978-3-642-14394-6.
- Astrm K.J. Introduction to stochastic control theory. Dover Publications, 2006. 320 p.
- Yurchenko I.V. The comparison theorem for the solution of the stochastic differential functional equations. Мiжнародна математична конференцiя, присвячена пам’ятi Ганса Гана. Матерiали. Чернiвцi: Рута, 1995. С. 322–332.
- Yasyns’kyi V.K., Sverdan M.L., Yurchenko I.V. On one problem of stochastic control. Ukrainian Mathematical Journal. 1995. Vol. 47, N 11. P. 1788–1797. https://doi.org/10.1007/BF01057927.
- Sverdan M.L., Tsarkov E.F., Yasynskyi V.K. Stability in stochastic modeling of complex dynamic systems [in Ukrainian]. Snyatyn: Nad Prutom, 1996. 448 p.
- Yasynskyi V.K., Yurchenko I.V. Stability and optimal control in stochastic dynamic systems with random operators [in Ukarainian]. The second edition, supplemented. Chernivtsi: Technodruk, 2019. 258 p.
