Improving Control-Performance Across AWGN Channels Using a Relay Node

Consider an unstable linear time invariant system in which the sensor transmits information to a controller across an additive white Gaussian noise channel. The designer can optionally utilize a relay node to assist the controller; however the total transmission power consumed by the sensor and the relay node is constant. The authors consider two topologies: a Gaussian relay channel, and a cascade of two Gaussian point to point channels. They propose coding schemes based on distributed stochastic approximation algorithms, and present sufficient conditions for the stabilizability of the plant through such schemes. The analysis suggests that it is useful to provide a relay node, even if the total transmission power remains the same.