ИСТИНА

We consider the problem to control a vibrating string to rest in a given finite time.The string is fixed at one end and controlled by Neumann or Dirichlet boundary control at the other end. We consider minimization of the boundary energy functional with inequality constraints on boundary control. Previously, the problem of minimizing the energy functional boundary was solved. However, the form of the explicit solution formula difficult to implement technically, because from the energy point of view our control can be divided into three parts: addition energy to the system to extinguish the initial state for a short period of time, then a long wait, and then adding energy to produce the final state to the set time T. We solve the problem of boundary control with a local restriction on adding energy: in any preassigned period of time energy management should not exceed the prescribed constant. We give an explicit repre- sentation of the L2-norm minimal control in terms of the given initial state and constant from local boundary energy constraints inequality.