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On controllability of a rotating string. (English) Zbl 1112.93008

The controllability of a rotating string is considered. Due to oscillations, the disk might hit the surrounding surfaces and lose the information that it carries. Hence, transverse oscillations should be minimized. A similar type of problem concerns the transversal oscillations of a rotating propeller of a helicopter which may cause dangerous situations for the plant. In case of a rotating string, a set of initial data is called controllable, if, for any initial data of this set, by suitable manipulation of the exterior force, the string goes to rest. The oscillations of the string are described by the wave equation. To get exact controllability in the sharp time interval, control functions from Sobolev spaces with noninteger indices are used. The results about the controllability are derived by means of the methods of moments.

MSC:

93B05 Controllability
93C95 Application models in control theory
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