TIME OPTIMAL CONTROL PROBLEM WITH INTEGRAL CONSTRAINT FOR THE HEAT TRANSFER PROCESS

In the present paper a mathematical model of thermocontrol processes is studied. Several convectors are installed on the disjoint subsets Гk 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 = ∪Γk, a heat exchange occurs by the Newton law. The control functions µk(t) 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

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