Geodesic
The Problem of Optimal Measurement of Considering Resonances: the Program Algorithm and Computer Experiment
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 13 (2012), pp. 58-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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This article describes a program that implements the algorithm of the numerical method for solving the problem of optimal measurement taking into account resonances — the problem of recovering dynamically distorted signal, taking into account the inertia of the measuring device and its mechanical resonances to be solved by using methods of optimal control theory. The basic idea behind the algorithm is to represent the numerical solution of the component measuring trigonometric polynomials, which reduces the problem of optimal control to the problem of convex programming in the unknown coefficients of polynomials. Using standard methods, such as gradient, in solving a convex programming problem, the complexity of the functional quality, leading to unsatisfactory results. It is therefore proposed a different, simpler method, which, together with the more laborious. This paper presents a number of solutions to improve computing speed, a block diagram of the basic procedure of a program written in C++, and the results of computer simulation models for a specific sensor.
Keywords: the problem of optimal measurement, optimal control, Leontief type systems, numerical solution, the program algorithm. 
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A. V. Keller; E. V. Zaharova. The Problem of Optimal Measurement of Considering Resonances: the Program Algorithm and Computer Experiment. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 13 (2012), pp. 58-68. http://geodesic.mathdoc.fr/item/VYURU_2012_13_a5/

[1] Shestakov A. L., “Measuring Transducer of the Dynamic Parameters of the Principle of Iterative Signal Restoration”, Instruments and Control Systems, 1992, no. 10, 23–24

[2] Shestakov A. L., Bizyaev M. N., “Recovery of Dynamically Distorted Signal Test and Measurement Systems Using Sliding Mode”, Izvestiya RAN, «Energy», 2004, no. 6, 119–130

[3] Shestakov A. L., Volosnikov A. S., “Neural Network Dynamic Model of a Measuring System with Filtering the Recovered Signal”, The Bulletin of the South-Ural State University. Seria «Computer Technology, Control, Electronics», 2006, no. 14 (69), issue 4, 16–20

[4] Shestakov A. L., Sviridyuk G. A., “A New Approach to Measuring Dynamically Distorted Signals”, Bulletin of South Ural State University. Seria «Mathematical Modelling, Programming Computer Software», 2010, no. 16(192), issue 5, 116–120 | Zbl

[5] Shestakov A. L., Keller A. V., Nazarova E. I., “Numerical Solution of Optimal Measurement”, Automatics and Telemechanics, 2012, no. 1, 107–115 | Zbl

[6] Keller A. V., Nazarova E. I., “The Problem of Optimal Measurement: a Numerical Solution, the Algorithm of the Program”, J. of News of Irkutsk State University. Seria «Mathematics», 4:3 (2011), 74–82 | Zbl

[7] Shestakov A. L., Sviridyuk G. A., “Optimal Dynamic Measurement of Distorted Signals”, Bulletin of South Ural State University. Seria «Mathematical Modelling, Programming Computer Software», 2011, no. 17(234), issue 8, 70–75 | Zbl

[8] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston–Köln–Tokyo, 2003 | MR | Zbl

[9] Keller A. V., “About the Algorithm for Solving Optimal Control and Hard Control”, Program Products and Systems, 2011, no. 3, 170–174

[10] Keller A. V., “Numerical Solution of the Problem Starting the Hard Management for Leontief Type Models. Computing Experiment”, Natural and Technical Sciences, 2011, no. 4, 476–482

[11] Sviridyuk G. A., Zagrebina S. A., “The problem Showalter–Sidorov as a Phenomenon of the Equations of Sobolev Type”, J. of News of Irkutsk State University. Seria «Mathematics», 3:1 (2010), 104–125 | MR | Zbl

[12] Zamyshlyaeva A. A., Yuzeeva A. V., “The Initial-Finite Value Problem for the Boussinesq–Löve Equation”, Bulletin of South Ural State University. Seria «Mathematical Modelling, Programming Computer Software», 2010, no. 16 (192), issue 5, 23–31 | Zbl

[13] Zagrebina S. A., “About Showalter–Sidorov Problem”, Russian Mathematics, 2007, no. 3, 22–28 | MR | Zbl

[14] Manakova N. A., Dylkov A. G., “About One Optimal Control Problem with the Functional Quality of the General Form”, Vestnik Samarakogo gosudarstvennogo tehnicheskogo universiteta. Seriya «Fiziko-matematicheskie nauki», 2011, no. 4(25), 18–24 | DOI