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Optimal control of one-dimensional heating with phase restrictions. (Russian. English summary) Zbl 0984.80013

Summary: The time-optimal control problem of heating one-dimensional bodies (plates, cylinders and balls) with restrictions on surface temperature and compressing and expanding thermotensions is considered. Control is achieved by means of boundary condition. An approximate solution method, based on approximation of input problem by finite-dimensional problem, is proposed. A numerical algorithm of solution of the finite-dimensional problem of Neustadt-Eaton type is proposed. The convergence of this algorithm is proved. Estimates of the rate of convergence for the square functional and estimates of errors in the presence phase restrictions are obtained. The results of of calculations in certain experiments are given.

MSC:

80M50 Optimization problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text: MNR