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Tr. Mat. Inst. Steklova, 2010, Volume 271, Pages 134–147 (Mi tm3243)  

On dynamical regularization under random noise

A. V. Kryazhimskiiab, Yu. S. Osipovc

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b International Institute for Applied Systems Analysis, Laxenburg, Austria
c Presidium of the Russian Academy of Sciences, Moscow, Russia

Abstract: We consider the problem of constructing a robust dynamic approximation of a time-varying input to a control system from the results of inaccurate observation of the states of the system. In contrast to the earlier studied cases in which the observation errors are assumed to be small in the metric sense, the errors in the present case are allowed to take, generally, large values and are subject to a certain probability distribution. The observation errors occurring at different instants are supposed to be statistically independent. Under the assumption that the expected values of the observation errors are small, we construct a dynamical algorithm for approximating the normal (minimal in the sense of the mean-square norm) input; the algorithm ensures an arbitrarily high level of the mean-square approximation accuracy with an arbitrarily high probability.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 271, 125–137

Bibliographic databases:

UDC: 517.977
Received in February 2010

Citation: A. V. Kryazhimskii, Yu. S. Osipov, “On dynamical regularization under random noise”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 134–147; Proc. Steklov Inst. Math., 271 (2010), 125–137

Citation in format AMSBIB
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\by A.~V.~Kryazhimskii, Yu.~S.~Osipov
\paper On dynamical regularization under random noise
\inbook Differential equations and topology.~II
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2010
\vol 271
\pages 134--147
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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