Optimal Local and Remote Controllers With Unreliable Uplink Channels: An Elementary Proof

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 nonclassical 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 nonlinear function of the observations). Their proof is based on a fairly sophisticated dynamic programming argument. In this article, we present an alternative and elementary proof of the result which uses common information-based conditional independence and completion of squares.