Robust control from data via uncertainty model sets identification

In this paper, an integrated robust identification and control design procedure is proposed. It is supposed that the plant to be controlled is linear, time invariant, stable, possibly infinite dimensional and that input-output noisy measurements are available, together with some general information on the plant and on the noise characteristics. The emphasis is laced on the design of controllers guaranteeing robust stability and robust performances, and on the trade off between controller complexity and achievable robust performances. First, an uncertainty model is identified, consisting of a parametric model and a tight frequency bound on the magnitude of the modeling error, accounting for the dynamics not modeled by the parametric model. Second, an Internal Model Control, guaranteeing robust closed loop stability and best approximating & the "perfect control" ideal target, is designed using H-infinity optimization techniques. This control structure is chosen because, if needed, it can be designed to be robust also in presence of input saturation. Then, the robust performances of the designed controller are computed, allowing to determine the level of model complexity needed to guarantee desired closed loop performances. A numerical example illustrates the effectiveness of the proposed design procedure.