Minimum-Information LQG Control - Part I: Memoryless Controllers

TL;DR

This paper develops an optimality principle for memoryless linear controllers in power-efficient feedback systems, balancing external control costs with minimal communication rates, and reveals their structural properties.

Contribution

It introduces a novel optimality principle for memoryless controllers that minimizes information rate while maintaining a specified external cost level.

Findings

Optimal memoryless controllers achieve minimal information rates.

The structure of optimal controllers includes order reduction.

The approach balances power efficiency with control performance.

Abstract

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.