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

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. We demonstrate that data-based covariance parameterization of the controller enables to incorporate bias-correction and instrumental variable techniques. This reduces 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.