Stochastic Model of Optimal Dynamic Measurements

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.

References

1. Belov A.A., Kurdyukov A.P. Descriptor Systems and Control Problems. Moscow, FIZMATLIT, 2015. (in Russian)
2. Khudyakov Yu.V. On Mathematical Modeling of the Measurement Transducers. Journal of Computational and Engineering Mathematics, 2016, vol. 3, no. 3, pp. 68-73. DOI: 10.14529/jcem160308
3. Granovsky V.A. Dynamic Measurements: Theory and Metrological Assurance at Yesterday and Tomorrow. Sensors and Systems, 2016, no. 3, pp. 57-72. (in Russian)
4. Ruhm K.H. Dynamics and Stability - A Proposal for Related Terms in Metrology from a Mathematical Point of View. Measurement: Journal of the International Measurement Confederation, 2016, vol. 79, pp. 276-284. DOI: 10.1016/j.measurement.2015.07.026
5. Shestakov A.L., Keller A.V., Sviridyuk G.A. Optimal Measurements. XXI IMEKO World Congress 'Measurement in Research and Industry', 2015, pp. 2072-2076.
6. Shestakov A.L., Sagadeeva M.A., Sviridyuk G.A. Reconstruction of a Dynamically Distorted Signal with Respect to the Measuring Transducer Degradation. Applied Mathematical Sciences, 2014, vol. 8, no. 41-44, pp. 2125-2130. DOI: 10.12988/ams.2014.312718
7. Keller A.V., Shestakov A.L., Sviridyuk G.A., Khudyakov Yu.V. The Numerical Algorithms for the Measurement of the Deterministic and Stochastic Signals. Springer Proceedings in Mathematics and Statistics, 2015, vol. 113, pp. 183-195. DOI: 10.1007/978-3-319-12145-1_11
8. Gliklikh Yu.E., Mashkov E.Yu. Stochastic Leontieff Type Equations and Mean Derivatives of Stochastic Processes. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2013, vol. 6, no. 2, pp. 25-39.
9. Shestakov A.L., Sviridyuk G.A., Khudyakov Yu.V. Dynamical Measurements in the View of the Group Operators Theory. Springer Proceedings in Mathematics and Statistics, 2015, vol. 113, pp. 273-286. DOI: 10.1007/978-3-319-12145-1_17
10. Zamyshlyaeva A.A., Sviridyuk G.A. The Linearized Benney - Luke Mathematical Model with Additive White Noise. Springer Proceedings in Mathematics and Statistics, 2015, vol. 113, pp. 327-337. DOI: 10.1007/978-3-319-12145-1_21
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, 2013, vol. 6, no. 1, pp. 20-34. (in Russian)
12. Favini A., Sviridyuk G.A., Manakova N.A. Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of 'Noises'. Abstract and Applied Analysis, 2015, vol. 2015, p. 697410. DOI: 10.1155/2015/697410
13. Khudyakov Yu.V. The Numerical Algorithm to Investigate Shestakov - Sviridyuk's Model of Measuring Device with Inertia and Resonances. Mathematical Notes of YSU, 2013, vol. 20, no. 2, pp. 211-221. (in Russian)