Optimal local and remote controllers with unreliable uplink channels: An elementary proof

TL;DR

This paper provides a simple, elementary proof for the optimal control strategies in a decentralized system with unreliable channels, improving understanding of such complex control problems.

Contribution

It introduces an elementary proof for the optimal control strategies in a decentralized system with unreliable uplink channels, replacing a complex dynamic programming approach.

Findings

Optimal control strategies are linear functions of the state estimate.

The proof uses common information based conditional independence.

The approach simplifies understanding of decentralized control with unreliable communication.

Abstract

Recently, a model of a decentralized control system with local and remote controllers connected over unreliable channels was presented in [1]. The model has a non-classical information structure that is not partially nested. Nonetheless, it is shown in [1] that the optimal control strategies are linear functions of the state estimate (which is a non-linear function of the observations). Their proof is based on a fairly sophisticated dynamic programming argument. In this note, we present an alternative and elementary proof of the result which uses common information based conditional independence and completion of squares.