棒材导热方程的Chernous'ko时间最优问题

Q3 Mathematics

Ural Mathematical Journal Pub Date : 2019-01-01 DOI:10.15826/UMJ.2019.1.002

A. Azamov, Jasurbek A. Bakhramov, O. S. Akhmedov

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引用次数: 2

摘要

研究了棒材导热系数可控方程的时间最优问题。通过傅里叶展开，将该问题简化为具有组合约束的一维控制系统的可数系统。为了改进由F.L. Chernous 'ko构造的次优控制的时间，采用了控制函数傅里叶展开的耦合项分组方法，得到了改进次优控制的显式综合。

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On the Chernous'ko Time-Optimal Problem for the Equation of Heat Conductivity in a Rod

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.

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来源期刊

Ural Mathematical Journal Mathematics-Mathematics (all)

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks