  We study a networked control architecture for linear time-invariant plants in
which an unreliable data-rate limited network is placed between the controller
and the plant input. The distinguishing aspect of the situation at hand is that
an unreliable data-rate limited network is placed between controller and the
plant input. To achieve robustness with respect to dropouts, the controller
transmits data packets containing plant input predictions, which minimize a
finite horizon cost function. In our formulation, we design sparse packets for
rate-limited networks, by adopting an an ell-0 optimization, which can be
effectively solved by an orthogonal matching pursuit method. Our formulation
ensures asymptotic stability of the control loop in the presence of bounded
packet dropouts. Simulation results indicate that the proposed controller
provides sparse control packets, thereby giving bit-rate reductions for the
case of memoryless scalar coding schemes when compared to the use of, more
common, quadratic cost functions, as in linear quadratic (LQ) control.
