Conditions for Complete Decentralization of the Linear Quadratic Regulator

TL;DR

This paper investigates the conditions under which Linear Quadratic Regulators can be fully decentralized, providing physical interpretations and extending results from simple to complex systems.

Contribution

It offers new conditions for complete decentralization of LQRs and interprets these conditions physically, bridging simple cases to more complex systems.

Findings

Identifies specific conditions for decentralization in simple LQR cases

Provides physical interpretations of decentralization conditions

Extends conditions to more complex systems

Abstract

An unconstrained optimal control policy is completely decentralized if computing actuation for each subsystem only requires information directly available to its own subcontroller. Parameters that admit a completely decentralized optimal controller have been characterized in a variety of systems, but attempts to physically explain the phenomenon have been limited. As a step toward a general characterization of complete decentralization, this paper presents conditions for complete decentralization of Linear Quadratic Regulators for several simple cases and physically interprets these conditions with illustrative examples. These simple cases are then leveraged to characterize complete decentralization of more complex systems.