  In this paper we consider the problem of controlling pointwise, by means of a
time dependent Dirac measure supported by a given point, a coupled system of
two Korteweg-de Vries equations on the unit circle. More precisely, by means of
spectral analysis and Fourier expansion we prove, under general assumptions on
the physical parameters of the system, a pointwise observability inequality
which leads to the pointwise controllability when we observe two control
functions. In addition, with a uniqueness property proved for the linearized
system without control, we are also able to show pointwise controllability when
only one control function acts internally. In both cases we can find, under
some assumptions on the coefficients of the system, the sharp time of the
controllability.
