Minimum-Information LQG Control — Part I: Memoryless Controllers

Roy Fox and Naftali Tishby

55th IEEE Conference on Decision and Control (CDC), 2016

With the increased demand for power efficiency in feedback-control systems, communication is becoming a limiting factor, raising the need to trade off the external cost that they incur with the capacity of the controller’s communication channels. With a proper design of the channels, this translates into a sequential rate-distortion problem, where we minimize the rate of information required for the controller’s operation, under a constraint on its external cost. Memoryless controllers are of particular interest, both for the simplicity and frugality of their implementation, and as a basis for studying more complex controllers. In this paper we present the optimality principle for memoryless linear controllers that utilize minimal information rates to achieve a guaranteed external cost level. We also study the interesting and useful phenomenology of the optimal controller, such as the principled reduction of its order.