Stochastic model of optimal dynamic measurements

Бесплатный доступ

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.

Еще

Stochastic problem, optimal dynamic measurement, cost functional

Короткий адрес: https://sciup.org/147232881

IDR: 147232881   |   DOI: 10.14529/mmp180212

Список литературы Stochastic model of optimal dynamic measurements

  • Белов, А.А. Дескрипторные системы и задачи управления / А.А. Белов, А.П. Курдюков. - M.: ФИЗМАТЛИТ, 2015. - 300 c.
  • Khudyakov, Yu.V. On Mathematical Modeling of the Measurement Transducers / Yu.V. Khudyakov // Journal of Computational and Engineering Mathematics. - 2016. - V. 3, № 3. - P. 68-73.
  • Грановский, В.А. Динамические измерения: теория и метрологическое обеспечение вчера и сегодня / В.А. Грановский // Датчики и системы. - 2016. - № 3. - C. 57-72.
  • Ruhm, K.H. Dynamics and Stability - A Proposal for Related Terms in Metrology from a Mathematical Point of View / K.H. Ruhm // Measurement: Journal of the International Measurement Confederation. - 2016. - V. 79. - P. 276-284.
  • Shestakov, A.L. Optimal Measurements / A.L. Shestakov, A.V. Keller, G.A. Sviridyuk // XXI IMEKO World Congress Measurement in Research and Industry. - 2015. - P. 2072-2076.
  • Shestakov, A.L. Reconstruction of a Dynamically Distorted Signal with Respect to the Measuring Transducer Degradation / A.L. Shestakov, M.A. Sagadeeva, G.A. Sviridyuk // Applied Mathematical Sciences. - 2014. - V. 8, № 41-44. - P. 2125-2130.
  • Keller, A.V. The Numerical Algorithms for the Measurement of the Deterministic and Stochastic Signals / A.V. Keller, A.L. Shestakov, G.A. Sviridyuk, Yu.V. Khudyakov // Springer Proceedings in Mathematics and Statistics. - 2015. - V. 113. - P. 183-195.
  • Gliklikh, Yu.E. Stochastic Leontieff Type Equations and Mean Derivatives of Stochastic Processes / Yu.E. Gliklikh, E.Yu. Mashkov // Вестник ЮУрГУ. Серия: Математическое моделирование и программирование. - 2013. - Т. 6, № 2. - С. 25-39.
  • Shestakov, A.L. Dynamical Measurements in the View of the Group Operators Theory / A.L. Shestakov, G.A. Sviridyuk, Yu.V. Khudyakov // Springer Proceedings in Mathematics and Statistics. - 2015. - V. 113. - P. 273-286.
  • Zamyshlyaeva, A.A. The linearized Benney - Luke Mathematical Model with Additive White Noise / A.A. Zamyshlyaeva, G.A. Sviridyuk // Springer Proceedings in Mathematics and Statistics. - 2015. - V. 113. - P. 327-337.
  • Загребина, С.А. Линейные уравнения соболевского типа с относительно p-ограниченными операторами и аддитивным белым шумом / С.А. Загребина, Е.А. Солдатова // Известия Иркутского государственного университета. Серия: Математика. - 2013. - Т. 6, № 1. - C. 20-34.
  • Favini, A. Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of "Noises" / A. Favini, G.A. Sviridyuk, N.A. Manakova // Abstract and Applied Analysis. - 2015. - V. 2015. - P. 697410.
  • Худяков, Ю.В. Алгоритм численного исследования модели Шестакова - Свиридюка измерительного устройства с инерционностью и резонансами / Ю.В. Худяков // Математические заметки ЯГУ. - 2013. - Т. 20, № 2. - С. 211-221.
Еще
Краткое сообщение