Direct data-driven controller design from bounded errors-in-variables measurements

The work focuses on direct data-driven controller design using input-output measurements corrupted by bounded additive noise. The main goal is to tackle the data-driven model reference control problem. To this end, we employ a set-membership framework and define the feasible controller parameter set, i.e., the set of parameters consistent with the noise bounds and the model-matching condition. We determine the controller parameters as the Chebyshev center of this set. We also provide a data-driven condition that is sufficient for establishing stability. This condition is also robust against the presence of bounded noise. The approach utilizes polynomial optimization and achieves global optimality via semidefinite relaxation techniques. A simulation example demonstrates the effectiveness of the proposed approach.