Data-driven parameterizations of suboptimal LQR and H2 controllers

TL;DR

This paper develops data-driven methods to design suboptimal LQR and H2 controllers for unknown linear systems, establishing conditions for data sufficiency and providing parameterizations of all such controllers, with insights on data quantity versus performance.

Contribution

It introduces novel data-driven parameterizations for suboptimal LQR and H2 controllers and identifies conditions for data sufficiency in controller design.

Findings

Numerical simulations demonstrate the trade-off between data samples and controller performance.

Conditions for data sufficiency are established for both control problems.

A comprehensive parameterization of all suboptimal controllers is provided.

Abstract

In this paper we design suboptimal control laws for an unknown linear system on the basis of measured data. We focus on the suboptimal linear quadratic regulator problem and the suboptimal H2 control problem. For both problems, we establish conditions under which a given data set contains sufficient information for controller design. We follow up by providing a data-driven parameterization of all suboptimal controllers. We will illustrate our results by numerical simulations, which will reveal an interesting trade-off between the number of collected data samples and the achieved controller performance.