On data-driven control: informativity of noisy input-output data with cross-covariance bounds

TL;DR

This paper advances data-driven control by developing new informativity conditions that incorporate cross-covariance bounds, enabling less conservative controller synthesis from noisy input-output data.

Contribution

It introduces a generalized noise characterization using cross-covariance bounds and extends informativity conditions for control based on input-output data.

Findings

Cross-covariance bounds can reduce conservativeness in data informativity.

The S-procedure remains applicable for non-quadratic noise bounds.

Simulation shows improved control performance with cross-covariance bounds.

Abstract

In this paper we develop new data informativity based controller synthesis methods that extend existing frameworks in two relevant directions: a more general noise characterization in terms of cross-covariance bounds and informativity conditions for control based on input-output data. Previous works have derived necessary and sufficient informativity conditions for noisy input-state data with quadratic noise bounds via an S-procedure. Although these bounds do not capture cross-covariance bounds in general, we show that the S-procedure is still applicable for obtaining non-conservative conditions on the data. Informativity-conditions for stability, $\mathcal{H}_\infty$ and $\mathcal{H}_2$ control are developed, which are sufficient for input-output data and also necessary for input-state data. Simulation experiments illustrate that cross-covariance bounds can be less conservative for informativity, compared to norm bounds typically employed in the literature.