  We consider a networked control system consisting of a remote controller and
a collection of linear plants, each associated with a local controller. Each
local controller directly observes the state of its co-located plant and can
inform the remote controller of the plant's state through an unreliable uplink
channel. We assume that the downlink channels from the remote controller to
local controllers are perfect. The objective of the local controllers and the
remote controller is to cooperatively minimize a quadratic performance cost. We
provide a dynamic program for this decentralized control problem using the
common information approach. Although our problem is not a partially nested
problem, we obtain explicit optimal strategies for all controllers. In the
optimal strategies, all controllers compute common estimates of the states of
the plants based on the common information obtained from the communication
network. The remote controller's action is linear in the common state
estimates, and the action of each local controller is linear in both the actual
state of its co-located plant and the common state estimates. We illustrate our
results with numerical experiments using randomly generated models.
