Geodesic
Reconstruction of distributed controls in parabolic systems by a~dynamic method
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 160-169

Voir la notice de l'article provenant de la source Math-Net.Ru

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, measurement, inverse problem, regularization, method of dynamic regularization
Mots-clés : reconstruction, observation, variation, piecewise uniform convergence. 
@article{TIMM_2013_19_1_a15,
     author = {A. I. Korotkii and D. O. Mikhailova},
     title = {Reconstruction of distributed controls in parabolic systems by a~dynamic method},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {160--169},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a15/}
}
TY  - JOUR
AU  - A. I. Korotkii
AU  - D. O. Mikhailova
TI  - Reconstruction of distributed controls in parabolic systems by a~dynamic method
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2013
SP  - 160
EP  - 169
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a15/
LA  - ru
ID  - TIMM_2013_19_1_a15
ER  - 
%0 Journal Article
%A A. I. Korotkii
%A D. O. Mikhailova
%T Reconstruction of distributed controls in parabolic systems by a~dynamic method
%J Trudy Instituta matematiki i mehaniki
%D 2013
%P 160-169
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a15/
%G ru
%F TIMM_2013_19_1_a15
A. I. Korotkii; D. O. Mikhailova. Reconstruction of distributed controls in parabolic systems by a~dynamic method. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 160-169. http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a15/