From noisy data to feedback controllers: non-conservative design via a matrix S-lemma

TL;DR

This paper introduces a novel matrix S-lemma enabling direct data-driven feedback controller design from noisy data, achieving non-conservative control methods for stabilization and H-infinity control with decision variables independent of data length.

Contribution

The paper presents a new matrix S-lemma and applies it to develop non-conservative, data-driven control design methods with decision variables independent of data horizon.

Findings

Derived data-based linear matrix inequalities for control design.

Achieved control design from large data sets without increasing decision variable complexity.

Provided strict and non-strict versions of the matrix S-lemma.

Abstract

We propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this paper. We provide both strict and non-strict versions of this S-lemma, that are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive non-conservative design methods for quadratic stabilization, H_2 and H_inf control, all in terms of data-based linear matrix inequalities. In contrast to previous work, the dimensions of our decision variables are independent of the time horizon of the experiment. Our approach thus enables control design from large data sets.