Dynamic Reconstruction of Disturbances in a Quasilinear Stochastic Differential Equation

The problem of reconstructing unknown inputs in a first-order quasilinear stochastic differential equation is studied by applying dynamic inversion theory. The disturbances in the deterministic and stochastic terms of the equation are simultaneously reconstructed using discrete information on some realizations of the stochastic process. The problem is reduced to an inverse one for ordinary differential equations satisfied by the expectation and variance of the original process. A finite-step software implementable solution algorithm is proposed, and its accuracy with respect to the number of measured realizations is estimated. An illustrative example is given.

Keywords

dynamic reconstruction, quasilinear stochastic differential equation, auxiliary controlled model

Received

11.10.2018

Publication date

11.10.2018

Number of characters

772

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GOST	Rozenberg V. Dynamic Reconstruction of Disturbances in a Quasilinear Stochastic Differential Equation // Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki – 2018. – V. 58. – Issue 7 C. 1121-1131 [Electronic resource]. URL: http://ras.jes.su/zvmmf/s207987840000703-2-1-en (circulation date: 18.04.2024). DOI: 10.31857/S004446690001461-8
MLA	Rozenberg, V. "Dynamic Reconstruction of Disturbances in a Quasilinear Stochastic Differential Equation." Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki 58.7 (2018):1121-1131. DOI: 10.31857/S004446690001461-8
APA	Rozenberg V. (2018). Dynamic Reconstruction of Disturbances in a Quasilinear Stochastic Differential Equation. Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki 58(7), pp.1121-1131 DOI: 10.31857/S004446690001461-8

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1. Kryazhimskij A.V., Osipov Yu.S. O modelirovanii upravleniya v dinamicheskoj sisteme // Izv. AN SSSR. Tekhn. kibernetika. 1983. 2. S. 51–60.

2. Osipov Yu.S., Kryazhimskii A.V. Inverse problems for ordinary differential equations: dynamical solutions. London: Gordon and Breach, 1995.

3. Maksimov V.I. Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem. Ekaterinburg: Izd-vo UrO RAN, 2000.

4. Osipov Yu.S., Kryazhimskij A.V., Maksimov V.I. Nekotorye algoritmy vosstanovleniya vkhodov // Tr. In-ta matematiki i mekhaniki UrO RAN. Ekaterinburg: IMM UrO RAN, 2011. T. 17, 1. C. 129–161.

5. Krasovskij N.N., Subbotin A.I. Pozitsionnye differentsial'nye igry. M.: Nauka, 1984.

6. Tikhonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnykh zadach. M.: Nauka, 1978.

7. Osipov Yu.S., Kryazhimskij A.V. Pozitsionnoe modelirovanie stokhasticheskogo upravleniya v dinamicheskikh sistemakh // Dokl. mezhdunar. konf. po stokhasticheskoj optimizatsii. Kiev, 1984. S. 43–45.

8. Rozenberg V.L. Zadacha dinamicheskogo vosstanovleniya neizvestnoj funktsii v linejnom stokhasticheskom differentsial'nom uravnenii // Avtomatika i telemekhanika. 2007. 11. S. 76–87.

9. Rozenberg V.L. Vosstanovlenie amplitudy sluchajnoj pomekhi v linejnom stokhasticheskom uravnenii po izmereniyam chasti koordinat // Zh. vychisl. matem. i matem. fiz. 2016. T. 56. 3. S. 377–386.

10. Rumyantsev D.S., Khrustalev M.M. Optimal'noe upravlenie kvazilinejnymi sistemami diffuzionnogo tipa pri nepolnoj informatsii o sostoyanii // Izvestiya RAN. Teoriya i sistemy upravleniya. 2006. № 5. S. 43–51.

11. Shiryaev A.N. Veroyatnost', statistika, sluchajnye protsessy. M.: Izd-vo MGU, 1974.

12. Oksendal' B. Stokhasticheskie differentsial'nye uravneniya. Vvedenie v teoriyu i prilozheniya. M.: Mir, 2003.

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

14. Chernous'ko F.L., Kolmanovskij V.B. Optimal'noe upravlenie pri sluchajnykh vozmuscheniyakh. M.: Nauka, 1978.

15. Johnson N.L., Kotz S., Balakrishnan N. Continuous univariate distributions. New York: John Wiley & Sons, 1995. Vol. 2.

16. Vdovin A.Yu. K zadache vosstanovleniya vozmuscheniya v dinamicheskoj sisteme. Dissertatsionnaya rabota...kand. fiz.-mat. nauk. Sverdlovsk: UrO AN SSSR, 1989.

17. Mil'shtejn G.N. Chislennoe integrirovanie stokhasticheskikh differentsial'nykh uravnenij. Sverdlovsk: Izd-vo UrGU, 1988.