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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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