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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 2, Pages 9–21 (Mi timm804)  

On the statistical stability of input identification problems for dynamic systems

S. A. Anikin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
References:
Abstract: An ill-posed problem of the reconstruction of input from measurements of output in a linear dynamic system is considered. Instead of the deterministic model of errors in the specification of input data, which is traditional for such problems, a stochastic model is proposed. More exactly, it is assumed that there is noise in the output measurement channel; the noise is modeled by realizations of a random element with a weak distribution in the space of outputs. To determine correctly the identification error, an extension of the space of outputs of the dynamic system is constructed. The notion of linear generalized solving procedure is introduced. Criteria for the statistic stability of the problem (the stability of the pseudo-inverse input-output operator of the system with respect to random errors in output measurements) are obtained.
Keywords: ill-posed problems, inverse problems of dynamics, statistical stability.
Received: 12.10.2011
Bibliographic databases:
Document Type: Article
UDC: 517.977+519.24+517.983.54
Language: Russian
Citation: S. A. Anikin, “On the statistical stability of input identification problems for dynamic systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 9–21
Citation in format AMSBIB
\Bibitem{Ani12}
\by S.~A.~Anikin
\paper On the statistical stability of input identification problems for dynamic systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 2
\pages 9--21
\mathnet{http://mi.mathnet.ru/timm804}
\elib{https://elibrary.ru/item.asp?id=17736182}
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