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With the increased demand for power efficiency in feedback-control systems,communication is becoming a limiting factor, raising the need to trade off theexternal cost that they incur with the capacity of the controller'scommunication channels. With a proper design of the channels, this translatesinto a sequential rate-distortion problem, where we minimize the rate ofinformation required for the controller's operation under a constraint on itsexternal cost. Memoryless controllers are of particular interest both for thesimplicity and frugality of their implementation and as a basis for studyingmore complex controllers. In this paper we present the optimality principle formemoryless linear controllers that utilize minimal information rates to achievea guaranteed external-cost level. We also study the interesting and usefulphenomenology of the optimal controller, such as the principled reduction ofits order.

Minimum-Information LQG Control - Part I: Memoryless Controllers