This work is concerned with control applications
over lossy data networks. Sensor data is transmitted to an
estimation-control unit over a network, and control commands
are issued to subsystems over the same network. Sensor and
control packets may be randomly lost according to a Bernoulli
process. In this context, the discrete-time Linear Quadratic
Gaussian (LQG) optimal control problem is considered.
For protocols where packets are acknowledged at the receiver
(e.g. TCP type protocols), the separation principle holds. Moreover, the optimal
LQG control is a linear function of the state.
We also show the existence
of critical arrival probabilities below which the optimal controller fails to stabilize
the system. This is done by providing analytic upper and lower bounds on the
cost functional, and stochastically characterizing their convergence properties in
the in¯nite horizon.
In the case where there is no feedback
on whether a control packet has been delivered or not (e.g. UDP type protocols),
the LQG optimal controller is in general nonlinear.
However, the simplicity of a linear sub-optimal solution is attractive for a
variety of applications. Accordingly, this paper characterizes
the optimal linear static controller and compares its performance
to the case when there is acknowledgement of delivery of packets.
Some novel results are also provided for the case where only a subset of the observation and control 
signals are lost when communicating across the network.