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.