Geodesic
On the problem of continuous estimation of a disturbance in a stochastic differential equation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 217-228
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Basing on the approach of the theory of dynamic inversion, the problem of continuous estimation of an unknown deterministic disturbance in an Ito stochastic differential equation is investigated with the use of inaccurate measurements of the current phase state. An auxiliary model equation with a control approximating the unknown input is derived. A suggested solving algorithm is constructive; its convergence rate estimate is explicitly written.
Keywords: continuous estimation of disturbance, stochastic differential equation, method of auxiliary models. 
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V. L. Rozenberg. On the problem of continuous estimation of a disturbance in a stochastic differential equation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 217-228. http://geodesic.mathdoc.fr/item/TIMM_2011_17_1_a17/

[1] Kryazhimskii A. V., Osipov Yu. S., “O modelirovanii upravleniya v dinamicheskoi sisteme”, Izv. AN SSSR. Tekhn. kibernetika, 1983, no. 2, 51–60 | MR

[2] Osipov Yu. S., Vasilev F. P., Potapov M. M., Osnovy metoda dinamicheskoi regulyarizatsii, Nauka, M., 1999, 238 pp.

[3] Osipov Yu. S., Kryazhimskii A. V., Inverse problems for ordinary differential equations: dynamical solutions, Gordon and Breach, London, 1995, 625 pp. | MR | Zbl

[4] Maksimov V. I., Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, Izd-vo UrO RAN, Ekaterinburg, 2000, 305 pp.

[5] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1984, 456 pp. | MR

[6] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1978, 142 pp.

[7] Maksimov V. I., “Uravneniya nepreryvnogo otsenivaniya vozmuschenii dinamicheskikh sistem”, Prikl. matematika i mekhanika, 70:5 (2006), 771–780 | MR | Zbl

[8] Osipov Yu. S., Kryazhimskii A. V., “Pozitsionnoe modelirovanie stokhasticheskogo upravleniya v dinamicheskikh sistemakh”, Dokl. mezhdunar. konf. po stokhasticheskoi optimizatsii, Kiev, 1984, 43–45

[9] Shiryaev A. N., Veroyatnost, statistika, sluchainye protsessy, Izd-vo MGU, M., 1974, 427 pp.

[10] Oksendal B., Stokhasticheskie differentsialnye uravneniya. Vvedenie v teoriyu i prilozheniya, Mir, M., 2003, 408 pp.

[11] Pugachev V. S., Sinitsyn I. N., Stokhasticheskie differentsialnye sistemy, Nauka, M., 1990, 642 pp. | MR | Zbl

[12] Rozenberg V. L., “Zadacha dinamicheskogo vosstanovleniya neizvestnoi funktsii v lineinom stokhasticheskom differentsialnom uravnenii”, Avtomatika i telemekhanika, 2007, no. 11, 76–87 | MR | Zbl

[13] Krasovskii N. N., Kotelnikova A. N., “Odna zadacha ob ustoichivom otslezhivanii dvizheniya”, Trudy Instituta matematiki i mekhaniki UrO RAN, 12, no. 1, 2006, 142–156 | MR | Zbl