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

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_k(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