Geodesic
On the Сhernous’ko time-optimal problem for the equation of heat conductivity in a rod
Ural mathematical journal, Tome 5 (2019) no. 1, pp. 13-23

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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.
Keywords: heat equation, time-optimal problem, Pontryagin maximum principle, suboptimal control, synthesis of control. 
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Abdulla A. Azamov; Jasurbek A. Bakhramov; Odiljon S. Akhmedov. On the Сhernous’ko time-optimal problem for the equation of heat conductivity in a rod. Ural mathematical journal, Tome 5 (2019) no. 1, pp. 13-23. http://geodesic.mathdoc.fr/item/UMJ_2019_5_1_a1/