an:01779329
Zbl 1001.49031
Golichev, I. I.; Dul'tsev, A. V.; Morozkin, N. D.
An iteration method for solving the problem of optimal nonlinear heating with phase constraints
EN
Comput. Math. Math. Phys. 40, No. 11, 1550-1566 (2000); translation from Zh. Vychisl. Mat. Mat. Fiz. 40, No. 11, 1615-1632 (2000).
00086076
2000
j
49M25 65M99 80M50 35B37 80A17 80M25
heating process; optimal control problem; method of successive approximation; iteration; nonlinear phase constraints; convergence
This paper is devoted to a one-dimensional time optimal control problem of heating process with constraints imposed on tension and compression thermal stresses and maximal temperature. An iteration method of solution is suggested based on reducing the initial nonlinear problem to a sequence of infinite-dimensional time optimal control problems described by linear state equations with nonlinear constraints on phase variables. It is proved that the sequence of solutions to these linear equations converges in the state to the solution of the initial nonlinear equation.
Alexey Tret'yakov (Siedlce)