On Infinite-horizon System Level Synthesis Problems

TL;DR

This paper develops a method for solving infinite-horizon distributed control and estimation problems directly in infinite-dimensional space, enabling optimal structured controllers and filters under communication constraints.

Contribution

It introduces a novel approach to infinite-horizon distributed LQG control and Kalman filtering without finite-impulse response relaxation, with practical implementation details.

Findings

Solves distributed LQG problems directly in infinite-dimensional space.

Constructs optimal distributed Kalman filters with limited communication.

Provides agent-level implementation for output-feedback controllers.

Abstract

System level synthesis is a promising approach that formulates structured optimal controller synthesis problems as convex problems. This work solves the distributed linear-quadratic regulator problem under communication constraints directly in infinite-dimensional space, without the finite-impulse response relaxation common in related work. Our method can also be used to construct optimal distributed Kalman filters with limited information exchange. We combine the distributed Kalman filter with state-feedback control to perform localized LQG control with communication constraints. We provide agent-level implementation details for the resulting output-feedback state-space controller.