Decentralized Control Problems with Substitutable Actions

TL;DR

This paper investigates decentralized control with substitutable actions, showing that under certain conditions, linear strategies are optimal and simplifying the design of controllers.

Contribution

It introduces the concept of substitutability in decentralized control and demonstrates its implications for optimal strategies in decentralized LQG problems.

Findings

Linear strategies are optimal under substitutability.

Complete state space characterization of optimal strategies.

Certain information structures yield the same cost as centralized control.

Abstract

We consider a decentralized system with multiple controllers and define substitutability of one controller by another in open-loop strategies. We explore the implications of this property on the optimization of closed-loop strategies. In particular, we focus on the decentralized LQG problem with substitutable actions. Even though the problem we formulate does not belong to the known classes of "simpler" decentralized problems such as partially nested or quadratically invariant problems, our results show that, under the substitutability assumption, linear strategies are optimal and we provide a complete state space characterization of optimal strategies. We also identify a family of information structures that all give the same optimal cost as the centralized information structure under the substitutability assumption. Our results suggest that open-loop substitutability can work as a counterpart of the information structure requirements that enable simplification of decentralized control problems.