Optimal control of one-dimensional heating with phase restrictions

The time-optimal control problem of heating of one-dimensional bodies (plates, cylinders and balls) with restrictions on surface temperature and compressing and expanding thermotensions is considered. The control througth boundary conditions is fulfilled. The approximate solution method, based on approximation of input problem by finite-dimensional problem, is proposed. The numerical algorithm of solution of 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 realization of phase restrictions are obtained. The results of calculating experiments are given.