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This paper is concerned with the existence of insensitizing controls for anonlinear coupled system of two Korteweg-de Vries (KdV) equations, typicallyknown as the Hirota-Satsuma system. The idea is to look for controls such thatsome functional of the states (the so-called sentinel) is insensitive to thesmall perturbations of initial data. Since the system is coupled, we consider asentinel in which we observe both components of the system in a localizedobservation set. By some classical argument, the insensitizing problem is thenreduced to a null-control problem for an extended system where the number ofequations is doubled. We study the null-controllability for the linearizedmodel associated to that extended system by means of a suitable Carlemanestimate which is proved in this paper. Finally, the local null-controllabilityof the extended (nonlinear) system is obtained by applying the inverse mappingtheorem, and this implies the required insensitizing property for the concernedmodel.

Insensitizing control problem for the Hirota-Satsuma system of KdV-KdV type