Abstract:
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.
Citation:
A. A. Zamyshlyaeva, A. V. Keller, M. B. Syropiatov, “Stochastic model of optimal dynamic measurements”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 11:2 (2018), 147–153
This publication is cited in the following 7 articles:
A. V. Keller, I. A. Kolesnikov, “Metody avtomaticheskogo i optimalnogo upravleniya v dinamicheskikh izmereniyakh”, J. Comp. Eng. Math., 10:4 (2023), 3–25
N. A. Manakova, O. V. Gavrilova, K. V. Perevozhikova, “Semilinear models of sobolev type. Non-uniqueness of solution to the Showalter–Sidorov problem”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 15:1 (2022), 84–100
E.V. Bychkov, S.A. Zagrebina, A.A. Zamyshlyaeva, N.A. Manakova, M.A. Sagadeeva, G.A. Sviridyuk, A.V. Keller, “Development of the Theory of Optimal Dynamic Measurements”, Bulletin of the SUSU. MMP, 15:3 (2022), 19
Olga G. Kitaeva, Dmitriy E. Shafranov, Georgy A. Sviridyuk, Springer Proceedings in Mathematics & Statistics, 325, Semigroups of Operators – Theory and Applications, 2020, 279
A. L. Shestakov, A. V. Keller, A. A. Zamyshlyaeva, N. A. Manakova, S. A. Zagrebina, G. A. Sviridyuk, “Teoriya optimalnykh izmerenii kak novaya paradigma metrologii”, J. Comp. Eng. Math., 7:1 (2020), 3–23
E. Yu. Mashkov, D. N. Tyutyunov, “Singulyarnye stokhasticheskie uravneniya leontevskogo tipa v terminakh tekuschikh skorostei resheniya”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:1 (2019), 55–65
O. G. Kitaeva, D. E. Shafranov, G. A. Sviridyuk, “Eksponentsialnye dikhotomii v modeli Barenblatta–Zheltova–Kochinoi v prostranstvakh differentsialnykh form s «shumami»”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:2 (2019), 47–57
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