LQG cheap control subject to packet loss and SNR limitations

In this paper we consider the problem of controlling unstable stochastic linear systems through a communication channel between the sensors and the actuators. We propose an LQG architecture which separates the design of suitable regulators, referred to as Plant Encoder/Decoders, from the design of the channel encoder/decoder. The mathematical model we propose encompasses the most important features of today's wireless channels such as limited channel capacity, decoding delay and packet loss, while still being amenable to analytic treatment. We then restrict our discussion to linear plant encoder/decoders subject to signal-to-noise (SNR) limitations and packet losses, deriving stability conditions and optimal parameters for the controller design in the cheap-control setting. Through our analysis we are able to recover several results available in the literature that treated packet loss and quantization error separately.