Rate of Prefix-free Codes in LQG Control Systems with Side Information

TL;DR

This paper investigates the tradeoff between communication cost and control performance in an LQG system with side information, proposing a convex optimization approach for designing prefix-free codes to optimize this balance.

Contribution

It introduces a novel convex optimization framework for designing prefix-free codes in LQG control systems with side information, addressing the tradeoff between communication cost and control quality.

Findings

Convex optimization method effectively balances communication cost and control performance.

Proposed quantizer design achieves near-optimal tradeoffs.

Achievability results demonstrate practical implementation feasibility.

Abstract

In this work, we study an LQG control system where one of two feedback channels is discrete and incurs a communication cost. We assume that a decoder (co-located with the controller) can make noiseless measurements of a subset of the state vector (referred to as side information) meanwhile a remote encoder (co-located with a sensor) can make arbitrary measurements of the entire state vector, but must convey its measurements to the decoder over a noiseless binary channel. Use of the channel incurs a communication cost, quantified as the time-averaged expected length of prefix-free binary codeword. We study the tradeoff between the communication cost and control performance. The formulation motivates a constrained directed information minimization problem, which can be solved via convex optimization. Using the optimization, we propose a quantizer design and a subsequent achievability result.