Optimal decentralized control of coupled subsystems with control sharing

TL;DR

This paper develops a three-step solution method for optimal decentralized control of coupled subsystems with shared control actions, extending previous work to finite-valued controls and providing an exact solution for a two-user system.

Contribution

It introduces a novel three-step approach for finite-valued control actions in control sharing scenarios, combining person-by-person, common information, and model-specific simplifications.

Findings

Three-step solution approach for finite-valued controls

Identification of sufficient statistics for local and shared information

Exact solution for a two-user multiple access broadcast system

Abstract

Subsystems that are coupled due to dynamics and costs arise naturally in various communication applications. In many such applications the control actions are shared between different control stations giving rise to a \emph{control sharing} information structure. Previous studies of control-sharing have concentrated on the linear quadratic Gaussian setup and a solution approach tailored to continuous valued control actions. In this paper a three step solution approach for finite valued control actions is presented. In the first step, a person-by-person approach is used to identify redundant data or a sufficient statistic for local information at each control station. In the second step, the common-information based approach of Nayyar et al.\ (2011) is used to find a sufficient statistic for the common information shared between all control stations and to obtain a dynamic programming decomposition. In the third step, the specifics of the model are used to simplify the sufficient statistic and the dynamic program. As an example, an exact solution of a two-user multiple access broadcast system is presented.