  This paper is concerned with the existence of insensitizing controls for a
nonlinear coupled system of two Korteweg-de Vries (KdV) equations, typically
known as the Hirota-Satsuma system. The idea is to look for controls such that
some functional of the states (the so-called sentinel) is insensitive to the
small perturbations of initial data. Since the system is coupled, we consider a
sentinel in which we observe both components of the system in a localized
observation set. By some classical argument, the insensitizing problem is then
reduced to a null-control problem for an extended system where the number of
equations is doubled. We study the null-controllability for the linearized
model associated to that extended system by means of a suitable Carleman
estimate which is proved in this paper. Finally, the local null-controllability
of the extended (nonlinear) system is obtained by applying the inverse mapping
theorem, and this implies the required insensitizing property for the concerned
model.
