We consider the problem of controlling a linear system with Gaussian noise and quadratic cost (LQG), using a memoryless controller that has limited capacity of the channel connecting its sensor to its actuator. We formulate this setting as a sequential rate-distortion (SRD) problem, where we minimize the rate of information required for the controller’s operation, under a constraint on its external cost. We present the optimality principle, and study the interesting and useful phenomenology of the optimal controller, such as the principled reduction of its order.

*Roy Fox and Naftali Tishby*, CDC 2016