An approximate solution to the decentralized two-controller infinite-horizon scalar LQG problem: Part II- slow dynamics

TL;DR

This paper extends previous work on decentralized scalar LQG problems, showing that for slow dynamics, linear strategies are nearly optimal among all distributed strategies in an infinite-horizon setting.

Contribution

It proves that in slow dynamics scenarios, simple linear strategies are approximately optimal for decentralized scalar LQG problems, expanding understanding of control strategies in such systems.

Findings

Linear strategies are constant ratio optimal in slow dynamics cases.

Linear strategies outperform other distributed strategies in the considered setting.

The result applies to infinite-horizon scalar LQG problems with two controllers.

Abstract

Continuing the first part of the paper, we consider scalar decentralized average-cost infinite-horizon LQG problems with two controllers. This paper focuses on the slow dynamics case when the eigenvalue of the system is small and prove that the single-controller optimal strategies ---linear strategies--- are constant ratio optimal among all distributed control strategies.