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 (Ural Mathematical Journal)
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.