A dynamic problem involving a coupled suspension bridge system: Numerical analysis and computational experiments
September 2019, 8(3): 473-488. doi: 10.3934/eect.2019023
Optimal control of solutions of a multipoint initial-final problem for non-autonomous evolutionary Sobolev type equation
Minzilia A. Sagadeeva , , Sophiya A. Zagrebina and Natalia A. Manakova
South Ural State University, Institute of Natural Sciences and Mathematics, 454080, Chelyabinsk, Lenin av, 76, Russian Federation
* Corresponding author: sagadeevama@susu.ru
Received January 2018 Revised November 2018 Published May 2019
Fund Project: The work was supported by Act 211 Government of the Russian Federation, contract 02.A03.21.0011
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The paper presents sufficient conditions for existence of an optimal control of solutions to a non-autonomous degenerate operator-differential evolution equation. We construct families of operators that solve this equation, as well as classical and strong solutions of the multipoint initial-final problem for the equation. We show that there exists a solution of an optimal control problem for a given operator-differential equation with a multipoint initial-final condition. The paper, in addition to the introduction and the bibliography, contains five sections. The first three parts contain information about the solvability of the multipoint initial-final problem for a non-autonomous equation. The fourth section presents the main result of the article; that is, a theorem on existence of optimal control of solutions to a multipoint initial-final problem. In the fifth part, the optimal control problem for the non-autonomous modified Chen – Gurtin model with the multipoint initial-final condition is investigated on the basis of the obtained abstract results.
Keywords: Relatively $ p $-radial operator, degenerate $ C_0 $-semiflow of solving operators, relatively spectral projections, generalized splitting theorem, strong solution, partial differential equation with complex coefficients.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Minzilia A. Sagadeeva, Sophiya A. Zagrebina, Natalia A. Manakova. Optimal control of solutions of a multipoint initial-final problem for non-autonomous evolutionary Sobolev type equation. Evolution Equations & Control Theory, 2019, 8 (3) : 473-488. doi: 10.3934/eect.2019023
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Minzilia A. Sagadeeva Sophiya A. Zagrebina Natalia A. Manakova