Minimum-Information LQG Control - Part I: Memoryless Controllers
For control engineers designing power-efficient feedback systems, this provides a theoretical foundation for trading off communication capacity against control cost.
This paper addresses the problem of minimizing the information rate required for memoryless linear controllers to achieve a guaranteed external-cost level in feedback-control systems. It establishes an optimality principle and reveals phenomena such as principled order reduction.
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.