  In this paper local exact controllability to the trajectories for the
one-dimensional monodomain equations with the FitzHugh-Nagumo and
Rogers-McCulloch ionic models using distributed controls with a moving support
is investigated. In a first step a new Carleman inequality for the adjoint of
the linearized monodomain equations, under assumptions on the movement of the
control region, is presented. It leads to null controllability at any positive
time. Subsequently, a local result concerning the exact controllability to the
trajectories for the nonlinear monodomain equations is deduced.
