Geodesic
Stochastic model of optimal dynamic measurements
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 2, pp. 147-153
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Under consideration is the stochastic model of optimal dynamic measurements. To solve this problem, the theory of optimal dynamic measurements which has actively been developing for the deterministic problems is extended to the stochastic case. The main purpose of the model is to restore a dynamically distorted input signal from a given observation using methods of the theory of dynamic measurements and the optimal control theory for Leontief type systems. Based on the results obtained by the authors earlier it is shown that optimal dynamic measurement as a minimum point of the cost functional doesn't depend on stochastic interference such as resonances in chains and random interference at the output of measuring transducer.
Keywords: stochastic problem; optimal dynamic measurement; cost functional. 
@article{VYURU_2018_11_2_a11,
     author = {A. A. Zamyshlyaeva and A. V. Keller and M. B. Syropiatov},
     title = {Stochastic model of optimal dynamic measurements},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {147--153},
     year = {2018},
     volume = {11},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2018_11_2_a11/}
}
TY  - JOUR
AU  - A. A. Zamyshlyaeva
AU  - A. V. Keller
AU  - M. B. Syropiatov
TI  - Stochastic model of optimal dynamic measurements
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2018
SP  - 147
EP  - 153
VL  - 11
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VYURU_2018_11_2_a11/
LA  - en
ID  - VYURU_2018_11_2_a11
ER  - 
%0 Journal Article
%A A. A. Zamyshlyaeva
%A A. V. Keller
%A M. B. Syropiatov
%T Stochastic model of optimal dynamic measurements
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2018
%P 147-153
%V 11
%N 2
%U http://geodesic.mathdoc.fr/item/VYURU_2018_11_2_a11/
%G en
%F VYURU_2018_11_2_a11
A. A. Zamyshlyaeva; A. V. Keller; M. B. Syropiatov. Stochastic model of optimal dynamic measurements. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 2, pp. 147-153. http://geodesic.mathdoc.fr/item/VYURU_2018_11_2_a11/

[1] Belov A. A., Kurdyukov A. P., Descriptor Systems and Control Problems, Fizmatlit, M., 2015 (in Russian)

[2] Yu.V. Khudyakov, “On Mathematical Modeling of the Measurement Transducers”, Journal of Computational and Engineering Mathematics, 3:3 (2016), 68–73 | DOI | MR

[3] Granovsky V. A., “Dynamic Measurements: Theory and Metrological Assurance at Yesterday and Tomorrow”, Sensors and Systems, 2016, no. 3, 57–72 (in Russian)

[4] K.H. Ruhm, “Dynamics and Stability – A Proposal for Related Terms in Metrology from a Mathematical Point of View”, Measurement: Journal of the International Measurement Confederation, 79 (2016), 276–284 | DOI

[5] A.L. Shestakov, A.V. Keller, G.A. Sviridyuk, “Optimal Measurements”, XXI IMEKO World Congress «Measurement in Research and Industry», 2015, 2072–2076

[6] A.L. Shestakov, M.A. Sagadeeva, G.A. Sviridyuk, “Reconstruction of a Dynamically Distorted Signal with Respect to the Measuring Transducer Degradation”, Applied Mathematical Sciences, 8:41–44 (2014), 2125–2130 | DOI

[7] A.V. Keller, A.L. Shestakov, G.A. Sviridyuk, Yu.V. Khudyakov, “The Numerical Algorithms for the Measurement of the Deterministic and Stochastic Signals”, Springer Proceedings in Mathematics and Statistics, 113 (2015), 183–195 | DOI | MR | Zbl

[8] Yu.E. Gliklikh, E.Yu. Mashkov, “Stochastic Leontieff Type Equations and Mean Derivatives of Stochastic Processes”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 6:2 (2013), 25–39 | MR | Zbl

[9] A.L. Shestakov, G.A. Sviridyuk, Yu.V. Khudyakov, “Dynamical Measurements in the View of the Group Operators Theory”, Springer Proceedings in Mathematics and Statistics, 113 (2015), 273–286 | DOI | MR | Zbl

[10] A.A. Zamyshlyaeva, G.A. Sviridyuk, “The linearized Benney–Luke Mathematical Model with Additive White Noise”, Springer Proceedings in Mathematics and Statistics, 113 (2015), 327–337 | DOI | MR | Zbl

[11] Zagrebina S. A., Soldatova E. A., “Linear Sobolev Type Equations with Relatively $p$-Bounded Operators and Additive White Noise”, News of Irkutsk State University. Series: Mathematics, 6:1 (2013), 20–34 (in Russian)

[12] A. Favini, G.A. Sviridyuk, N.A. Manakova, “Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises””, Abstract and Applied Analysis, 2015 (2015), 697410 | DOI | MR | Zbl

[13] Khudyakov Yu.V., “The Numerical Algorithm to Investigate Shestakov–Sviridyuk's Model of Measuring Device with Inertia and Resonances”, Mathematical Notes of YSU, 20:2 (2013), 211–221 (in Russian) | Zbl