  In this paper, we consider a class of mechanical models which consists of a
linear chain of identical chaotic cells, each of which has two small lateral
holes and contains a rotating disk at its center. Particles are injected at
characteristic temperatures and rates from stochastic heat baths located at
both ends of the chain. Once in the system, the particles move freely within
the cells and will experience elastic collisions with the outer boundary of the
cells as well as with the disks. They do not interact with each other but can
transfer energy from one to another through collisions with the disks. The
state of the system is defined by the positions and velocities of the particles
and by the angular positions and angular velocities of the disks. We show that
each model in this class is controllable with respect to the baths, i.e. we
prove that the action of the baths can drive the system from any state to any
other state in a finite time. As a consequence, one obtains the existence of at
most one regular invariant measure characterizing its states (out of
equilibrium).
