Bias correction and instrumental variables for direct data-driven model-reference control

TL;DR

This paper introduces a scalable data-driven control method for LTI systems that employs bias correction and instrumental variables to mitigate noise effects, ensuring effective controller synthesis from noisy data.

Contribution

It presents a novel noise mitigation technique using data-based covariance parameterization, enabling bias correction and instrumental variables in data-driven control design.

Findings

Reduces measurement noise impact as data volume increases.

Number of decision variables remains independent of dataset size.

Demonstrated effectiveness through a numerical example.

Abstract

Managing noisy data is a central challenge in direct data-driven control design. We propose an approach for synthesizing model-reference controllers for linear time-invariant (LTI) systems using noisy state-input data, employing novel noise mitigation techniques. Specifically, we demonstrate that using data-based covariance parameterization of the controller enables bias-correction and instrumental variable techniques within the data-driven optimization, thus reducing measurement noise effects as data volume increases. The number of decision variables remains independent of dataset size, making this method scalable to large datasets. The approach's effectiveness is demonstrated with a numerical example.