Control over a network: Using actuation buffers to reduce transmission frequency

We consider a discrete time linear feedback control system with additive noise where the control signals are sent across a network from the controller to the actuators. Due to network considerations it is desired to reduce the transmission frequency of the control signals. We show that by including a finite sequence of predicted control signals in each communication packet the frequency of transmission can be reduced by transmitting only when the previously sent sequence has run out, although as a consequence the closed loop error will increase. We introduce a communication protocol, which we call Input Difference Transmission Scheme (IDTS), that transmits control packets when the difference between newly computed control values and the predicted control sequence previously transmitted is larger than a certain threshold. This threshold is a design parameter and we show how the closed loop behavior varies with this threshold. Simulation results are provided to augment the theory.