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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 1, Pages 160–169
(Mi timm910)
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This article is cited in 1 scientific paper (total in 1 paper)
Reconstruction of distributed controls in parabolic systems by a dynamic method
A. I. Korotkiiab, D. O. Mikhailovab a Ural Federal University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
We consider the problem of reconstructing a priori unknown distributed controls in parabolic systems from results of approximate measurements of states of the system's observed motion. The problem is solved in the dynamic variant, when a current approximation of the unknown control is found only from the measurements received no later than the current time. The problem under consideration is ill-posed. We propose to solve it by the method of dynamic regularization and construct new dynamic regularization algorithms, which provide a strengthened convergence of regularized approximations, in particular, their piecewise uniform convergence. A finite-dimensional approximation of the problem is carried out and results of numerical simulation are presented.
Keywords:
dynamic system, control, reconstruction, observation, measurement, inverse problem, regularization, method of dynamic regularization, variation, piecewise uniform convergence.
Received: 22.10.2012
Citation:
A. I. Korotkii, D. O. Mikhailova, “Reconstruction of distributed controls in parabolic systems by a dynamic method”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 1, 2013, 160–169
Linking options:
https://www.mathnet.ru/eng/timm910 https://www.mathnet.ru/eng/timm/v19/i1/p160
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Abstract page: | 391 | Full-text PDF : | 98 | References: | 64 | First page: | 10 |
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