Localized LQG optimal control for large-scale systems

This paper poses and solves the localized linear quadratic Gaussian (LLQG) optimal control problem. In particular, we show that for large-scale localizable systems, that is to say systems for which the closed loop effect of each disturbance can be contained to within a local neighborhood despite communication delays between sub-controllers, the synthesis and implementation of a LLQG optimal controller can be performed in a scalable way. We combine our prior results on the state-feedback version of this problem with the alternating direction method of multipliers (ADMM) algorithm to formulate a synthesis algorithm that can be solved in a distributed fashion, with each subsystem solving a problem of constant dimension independent of the global problem size. The result is a controller synthesis and implementation scheme that can scale to systems of arbitrary dimension, subject to certain conditions on the communication, actuation and sensing schemes holding. Simulations show that for some systems, the LLQG optimal controller can achieve transient performance similar to that of a centralized H
₂
optimal controller. We also demonstrate our algorithm on a system with about 104 states composed of heterogeneous and dynamically coupled subsystems - here the distributed and centralized optimal controllers cannot be computed.