# Time optimal control problem with integral constraint for the heat transfer process

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## Keywords:

heat transfer process, control function, integral constraint, optimal control, optimal time## Abstract

In the present paper a mathematical model of thermocontrol processes is studied. Several convectors are installed on the disjoint subsets Г_{k} of the wall ∂Ω of a volume Ω and each convector produces a hot or cold flow with magnitude equal to µk(t), which are control functions, and on the surface *∂Ω \ Γ, Γ = ∪Γ _{k}*, a heat exchange occurs by the Newton law. The control functions

*µ*are subjected to an integral constraint. The problem is to find control functions to transfer the state of the process to a given state. A necessary and sufficient condition is found for solvability of this problem. An equation for the optimal transfer time is found, and an optimal control function is constructed explicitly

_{k}(t)## Downloads

## Published

## How to Cite

*Eurasian Mathematical Journal*,

*15*(1). Retrieved from https://emj.enu.kz/index.php/main/article/view/3