Robust Data-Driven Control for Systems with Noisy Data: arXiv:2207.09587 [math.OC]

This paper presents a robust data-driven controller design based on the noisy input-output data without assumptions on the statistical properties of the noises. We start with the direct data-representation of system models that take elements from behavioral system theory, followed by analyses of the upper bound of the "modeling" error with the data representation with presence of noises. Some pre-conditioning methods are put into the context based on how the derived bound is structured. We lastly leverage the upper bound to develop robust controllers that ride through the data noises.