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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 1, Pages 161–166 (Mi tvp697)

Short Communications

The Use of the Integral Functional in Some Methods of Control in the Presence of Small Random Perturbations

A. P. Cherenkov

Moscow

Abstract: The problems described in [1] and [2] (parametric control and control by means of a single switching) are considered with the difference that the characterizing function is replaced by the characterizing functional of the integral type. In both cases we prove the existence of the minimum of the variance of some functional and evaluate this minimum. The minimizing functions are also determined. Necessary and sufficient conditions for this minimum to be equal to zero are given.

Full text: PDF file (355 kB)

English version:
Theory of Probability and its Applications, 1967, 12:1, 139–143

Bibliographic databases:

Citation: A. P. Cherenkov, “The Use of the Integral Functional in Some Methods of Control in the Presence of Small Random Perturbations”, Teor. Veroyatnost. i Primenen., 12:1 (1967), 161–166; Theory Probab. Appl., 12:1 (1967), 139–143

Citation in format AMSBIB
\Bibitem{Che67} \by A.~P.~Cherenkov \paper The Use of the Integral Functional in Some Methods of Control in the Presence of Small Random Perturbations \jour Teor. Veroyatnost. i Primenen. \yr 1967 \vol 12 \issue 1 \pages 161--166 \mathnet{http://mi.mathnet.ru/tvp697} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=210498} \zmath{https://zbmath.org/?q=an:0183.19404|0147.16102} \transl \jour Theory Probab. Appl. \yr 1967 \vol 12 \issue 1 \pages 139--143 \crossref{https://doi.org/10.1137/1112018}