Minimum-Information LQG Control - Part II: Retentive Controllers

TL;DR

This paper formulates the problem of retentive control with communication constraints as a rate-distortion problem, extending previous work to include memory components and analyzing the structure of optimal solutions.

Contribution

It extends the minimum-information LQG control framework to retentive controllers with memory, reducing the problem to a memoryless case and exploring optimal solution structures.

Findings

Optimal retentive controllers can be characterized via a rate-distortion framework.

The problem reduces to a memoryless control problem by modeling memory operations as sensors and actuators.

The structure of optimal solutions exhibits interesting phenomenology.

Abstract

Retentive (memory-utilizing) sensing-acting agents may operate under limitations on the communication between their sensing, memory and acting components, requiring them to trade off the external cost that they incur with the capacity of their communication channels. In this paper we formulate this problem as a sequential rate-distortion problem of minimizing the rate of information required for the controller's operation under a constraint on its external cost. We reduce this bounded retentive control problem to the memoryless one, studied in Part I of this work, by viewing the memory reader as one more sensor and the memory writer as one more actuator. We further investigate the structure of the resulting optimal solution and demonstrate its interesting phenomenology.