Abstract.

Many practical problems in mathematical formulation are reduced to the problems which require to transfer the system from one state to given another one. These problems are usually called time optimal problems and are investigated in the mathematical theory of optimal processes. For the systems with the distributed parameters, these investigations meet serious dificulties in differ from the systems with the concentrated parameters. Time optimal problems arise in various technological processes, which are described by the equations of heat conductivity, diffusions, filtrations. For example, time optimal problem appears in the control of diffusion process of neutrons in the nuclear reactor. Until now, mainly the problems with classical boundary conditions have been considered [2, 4, 5, 8, 9, 10].

Keywords:

time optimal control, spectral problem, relay, necessary condition, generalized solu- tion.