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Russia Yekaterinburg
Section Mathematics
Title Reconstruction of the right-hand part of a distributed differential equation using a positional controlled model
Author(-s) Blizorukova M.S.a, Maksimov V.I.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa
Abstract In this paper, we consider the stable reconstruction problem of the unknown input of a distributed system of second order by results of inaccurate measurements of its solution. The content of the problem considered is as follows. We consider a distributed equation of second order. The solution of the equation depends on the input varying in the time. The input, as well as the solution, is not given in advance. At discrete times the solution of the equation is measured. These measurements are not accurate in general. It is required to design an algorithm for approximate reconstruction of the input that has dynamical and stability properties. The dynamical property means that the current values of approximations of the input are produced on-line, and the stability property means that the approximations are arbitrarily accurate for a sufficient accuracy of measurements. The problem refers to the class of inverse problems. The algorithm presented in the paper is based on the constructions of a stable dynamical inversion and on the combination of the methods of ill-posed problems and positional control theory.
Keywords dynamical inversion, distributed system
UDC 517.71
MSC 49J35, 91A24
DOI 10.35634/vm200401
Received 3 September 2020
Language Russian
Citation Blizorukova M.S., Maksimov V.I. Reconstruction of the right-hand part of a distributed differential equation using a positional controlled model, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 4, pp. 533-552.
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