Optimal feedback control problem for Bingham media motion with periodic boundary conditions

2019 ◽  
Vol 485 (2) ◽  
pp. 139-141
Author(s):  
V. G. Zvyagin ◽  
M. V. Turbin
Keyword(s):  
Feedback Control ◽  
Boundary Conditions ◽  
Control Problem ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
Degree Theory ◽  
Periodic Boundary Conditions ◽  
Optimal Feedback Control ◽  
Operator Inclusion ◽  
Optimal Feedback

We study the optimal feedback control problem for the motion of Bingham media with periodic boundary conditions in two- and three-dimensional cases. First, the considered problem is interpreted as an operator inclusion with a multivalued right-hand side. Then, the approximation-topological approach to hydrodynamic problems and the degree theory for a class of multivalued maps are used to prove the existence of solutions of this inclusion. Finally, we prove that, among the solutions of the considered problem, there exists one minimizing the given cost functional.

scholarly journals The existence theorem for weak solution of optimal feedback control problem for the modified Kelvin-Voigt model of weakly concentrated aqueous polymer solutions

2019 ◽  
Vol 488 (2) ◽  
pp. 133-136
Author(s):  
P. I. Plotnikov ◽  
M. V. Turbin ◽  
A. S. Ustiuzhaninova
Keyword(s):  
Weak Solution ◽  
Feedback Control ◽  
Control Problem ◽  
Existence Theorem ◽  
Polymer Solutions ◽  
Optimal Feedback Control ◽  
Operator Inclusion ◽  
Optimal Feedback ◽  
Aqueous Polymer ◽  
Voigt Model

In this paper the existence theorem on weak solution of the optimal feedback control problem for the modified Kelvin-Voigt model of weakly concentrated aqueous polymer solutions. The proof is carried out on the basis of an approximation-topological approach to the study of fluid dynamic problems. At the first step, the considered feedback control problem is interpreted as an operator inclusion with a multi-valued right-hand side. In the second step, the resulting inclusion is approximated by an operator inclusion with better properties. Then, on the basis of a priori estimates of solutions and the degree theory of a class of multi-valued mappings, the existence of solutions for this inclusion is proved. In the third step, it is shown that from the sequence of solutions of the approximation inclusion one can extract a subsequence that converges weakly to the solution of the original inclusion. Then it is proved that among the solutions of the considered problem there is a solution that gives a minimum to a given quality functional.

scholarly journals Optimal Feedback Control Problem for the Fractional Voigt-α Model

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1197
Author(s):  
Victor Zvyagin ◽  
Andrey Zvyagin ◽  
Anastasiia Ustiuzhaninova
Keyword(s):  
Velocity Field ◽  
Feedback Control ◽  
Control Problem ◽  
Fluid Dynamic ◽  
Optimal Solution ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Optimal Feedback Control ◽  
Optimal Feedback ◽  
Liouville Derivative

The study of the existence of an optimal feedback control problem for the initial-boundary value problem that describes the motion of the fractional Voigt- α model of a viscoelastic medium is investigated in this paper. In this model, the Voigt rheological relation is considered with the left-side fractional Riemann-Liouville derivative, which allows to take into account the memory of the medium. Also in this model, the memory is considered along the trajectory of the motion of fluid particles, determined by the velocity field. Due to the insufficient smoothness of the velocity field and, as a consequence, the impossibility of uniquely determining the trajectory for the velocity field for any initial value, a weak solution to the problem under study is introduced using regular Lagrangian flows. Based on the approximation-topological approach to the study of fluid dynamic problems, the existence of an optimal solution that gives a minimum to a given cost functional is proved.

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