  The purpose of this article is the investigation of the global control
properties of a coupled nonlinear dispersive system posed in the periodic
domain $\mathbb{T}$, a system with structure of a nonlinear Schr\"odinger
equation and a nonlinear Korteweg-de Vries equation. Combining estimates
derived from Bourgain spaces and using microlocal analysis we show that this
system has global control properties. The main novelty of this work is in
twofold. One is that the global results for the nonlinear system are presented
for the first time thanks to the propagation of singularities. The second one
is that these propagation results are shown to a coupled dispersive system with
two equations defined by differential operators with principal symbols of
different orders.
