Minimax Theory and its Applications 05 (2020), No. 2, 439--454
Copyright Heldermann Verlag 2020
Hamiltonian Systems for Control Reconstruction Problems
Nina N. Subbotina
Krasovskii Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, Yekaterinburg 620108, Russia;
and: Ural Federal University, Yekaterinburg 620002, Russia
subb@uran.ru
Evgenii A. Krupennikov
Krasovskii Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, Yekaterinburg 620108, Russia;
and: Ural Federal University, Yekaterinburg 620002, Russia
krupennikov@imm.uran.ru
We present and justify a new algorithm for solving dynamic reconstruction problems. The algorithm is based on solutions of Hamiltonian systems that arise in auxiliary variational problems with concave-convex discrepancy functionals. Modifications of Hamiltonian systems, improving the effectiveness of the new algorithm, are suggested and justified. Results of numerical solution of a reconstruction problem in medicine are reported.
Keywords: Dynamic reconstruction problems, convex-concave discrepancy, variational problems, Hamiltonian systems.
MSC: 65L09, 49K15, 90C26.
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