Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems

TL;DR

This paper establishes a sample complexity bound for learning robust LQG controllers in partially observed systems with unknown dynamics, using a model estimation and robust synthesis approach based on Input-Output Parameterization.

Contribution

It introduces a novel end-to-end sample complexity analysis for LQG control with unknown dynamics, leveraging convex optimization and robust synthesis techniques.

Findings

Performance degrades linearly with estimation error

Sample complexity matches LQR results despite hidden states

Robust controller design via Input-Output Parameterization

Abstract

This paper studies a class of partially observed Linear Quadratic Gaussian (LQG) problems with unknown dynamics. We establish an end-to-end sample complexity bound on learning a robust LQG controller for open-loop stable plants. This is achieved using a robust synthesis procedure, where we first estimate a model from a single input-output trajectory of finite length, identify an H-infinity bound on the estimation error, and then design a robust controller using the estimated model and its quantified uncertainty. Our synthesis procedure leverages a recent control tool called Input-Output Parameterization (IOP) that enables robust controller design using convex optimization. For open-loop stable systems, we prove that the LQG performance degrades linearly with respect to the model estimation error using the proposed synthesis procedure. Despite the hidden states in the LQG problem, the achieved scaling matches previous results on learning Linear Quadratic Regulator (LQR) controllers with full state observations.