Optimal control of solutions of a multipoint initial-final problem for non-autonomous evolutionary Sobolev type equation

Minzilia A. Sagadeeva; Sophiya A. Zagrebina; Natalia A. Manakova

doi:10.3934/eect.2019023

Article Contents

2019, Volume 8, Issue 3: 473-488. Doi: 10.3934/eect.2019023

This issue Previous Article Next Article A dynamic problem involving a coupled suspension bridge system: Numerical analysis and computational experiments

Optimal control of solutions of a multipoint initial-final problem for non-autonomous evolutionary Sobolev type equation

South Ural State University, Institute of Natural Sciences and Mathematics, 454080, Chelyabinsk, Lenin av, 76, Russian Federation

^* Corresponding author: sagadeevama@susu.ru
^* Corresponding author: sagadeevama@susu.ru

Received: December 31, 2017

Revised: October 31, 2018

Early access: May 2019

Published: August 2019

The work was supported by Act 211 Government of the Russian Federation, contract 02.A03.21.0011.

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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