# Formulas for Data-driven Control: Stabilization, Optimality and Robustness

## TL;DR

This paper introduces a data-driven approach for control design that uses persistently exciting data to solve stabilization and optimal control problems via Linear Matrix Inequalities without explicit system identification.

## Contribution

It derives a parametrization of linear feedback systems based solely on data, enabling control solutions without needing to identify system matrices beforehand.

## Key findings

- Successfully stabilizes linear systems using data-driven methods.
- Solves linear quadratic regulation problems with data-based techniques.
- Addresses robustness to measurement noise and nonlinear system stabilization.

## Abstract

In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent Linear Matrix Inequalities only. The result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state and output feedback stabilization, and the linear quadratic regulation problem. We also discuss robustness to noise-corrupted measurements and show how the approach can be used to stabilize unstable equilibria of nonlinear systems.