LQG Control under Limited Communication

We discuss Kalman filtering and LQ optimal control of a networked control system (NCS) whose sensors and actuators exchange information with a remote controller over a shared communication medium. Access to that medium is governed by a pair of periodic communication sequences. Under the proposed model, the controller and plant handle communication disruptions by "ignoring" sensors and actuators that are not actively communicating. We show that Kalman filtering and LQ optimal control for NCSs can be formulated as a standard LQG problem for an equivalent periodic system. Moreover, under mild conditions, there always exist periodic communication sequences that preserve the detectability and observability of the NCS and thus make it possible to guarantee the existence of a stabilizing LQG controller.