The Optimal Feedback Control Problem for Voigt Model with Variable Density

The work is devoted to the study of weak solvability of the optimal feedback control problem for the Voigt model with variable density. The proof is based on the approximation-topological approach. First, the solvability of the approximation problem is proved, and then, based on a priori estimates t...

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Bibliographic Details
Published inRussian mathematics Vol. 64; no. 4; pp. 80 - 84
Main Authors Zvyagin, V. G., Turbin, M. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.04.2020
Springer Nature B.V
Subjects
Approximation
Brief Communications
Control systems
Density
Feedback control
Mathematics
Mathematics and Statistics
feedback
optimal control problem
weak solution
approximation-topological approach
nonhomogeneous fluid
Voigt model
variable-density fluid
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Summary:The work is devoted to the study of weak solvability of the optimal feedback control problem for the Voigt model with variable density. The proof is based on the approximation-topological approach. First, the solvability of the approximation problem is proved, and then, based on a priori estimates that are independent of the approximation parameter, it is shown that from the sequence of solutions of the approximation problem, a subsequence converging to the solution of the original problem can be chosen. Then it is shown that among weak solutions to the problem there is at least one that gives a minimum to a given cost functional.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X2004009X