Stochastic linear control over a communication channel

We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular, we examine the role communication has on the classical linear quadratic Gaussian problem. We give conditions under which the classical separation property between estimation and control holds and the certainty equivalent control law is optimal. We then present the sequential rate distortion framework. We present bounds on the achievable performance and show the inherent tradeoffs between control and communication costs. In particular, we show that optimal quadratic cost decomposes into two terms: A full knowledge cost and a sequential rate distortion cost.