Zur zeitminimalen Randsteuerung einer homogenen schwingenden Saite

Abstract

In this paper the following problem is considered: A homogeneous vibrating string which is clamped at one end has to be steered into a position of permanent rest by a boundary control. Given an initial state of vibration and a bound for the norm of the control, a minimum time and a corresponding time minimal control have to be determined. This problem turns out to be equivalent to a moment problem which can be solved easily, due to its special structure. Essentially only one transcendental equation in one variable has to be solved for determining the required time and the corresponding control. Numerical results are presented at the end of the paper.