ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD

Abdulla A. Azamov; Jasurbek A. Bakhramov; Odiljon S. Akhmedov

doi:10.15826/umj.2019.1.002

Ural Mathematical Journal (Jul 2019)

ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD

Abdulla A. Azamov,
Jasurbek A. Bakhramov,
Odiljon S. Akhmedov

Affiliations

Abdulla A. Azamov: Institute of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Durmon yuli st., 29 Tashkent, 100125
Jasurbek A. Bakhramov: Institute of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Durmon yuli st., 29 Tashkent, 100125
Odiljon S. Akhmedov: Institute of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Durmon yuli st., 29 Tashkent, 100125

DOI: https://doi.org/10.15826/umj.2019.1.002
Journal volume & issue: Vol. 5, no. 1

Abstract

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The time-optimal problem for the controllable equation of heat conductivity in a rod is considered. By means of the Fourier expansion, the problem reduced to a countable system of one-dimensional control systems with a combined constraint joining control parameters in one relation. In order to improve the time of a suboptimal control constructed by F.L. Chernous'ko, a method of grouping coupled terms of the Fourier expansion of a control function is applied, and a synthesis of the improved suboptimal control is obtained in an explicit form.

Heat equation, Time-optimal problem, Pontryagin maximum principle, Suboptimal control, Synthesis of control

Published in Ural Mathematical Journal

ISSN: 2414-3952 (Online)
Publisher: Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
Country of publisher: Russian Federation
LCC subjects: Science: Mathematics
Website: https://umjuran.ru

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