Exact controllability of the transmission string–beam equations with a single boundary control

Abstract

We consider the exact controllability of a transmission system which models a flexible beam with one end clamped and the other end linked to a string. The control only acts on the free end of the string. Using the multiplier method, we prove that the full energy of transmission system can be estimated by the boundary data of string. Finally, by using the HUM method, we deduce that the transmission system is exactly controllable at the time of control .