  The theory of covariance control and covariance steering (CS) deals with
controlling the dispersion of trajectories of a dynamical system, under the
implicit assumption that accurate prior knowledge of the system being
controlled is available. In this work, we consider the problem of steering the
distribution of a discrete-time, linear system subject to exogenous
disturbances under an unknown dynamics model. Leveraging concepts from
behavioral systems theory, the trajectories of this unknown, noisy system may
be (approximately) represented using system data collected through
experimentation. Using this fact, we formulate a direct data-driven covariance
control problem using input-state data. We then propose a maximum likelihood
uncertainty quantification method to estimate and bound the noise realizations
in the data collection process. Lastly, we utilize robust convex optimization
techniques to solve the resulting norm-bounded uncertain convex program. We
illustrate the proposed end-to-end data-driven CS algorithm on a double
integrator example and showcase the efficacy and accuracy of the proposed
method compared to that of model-based methods
