Robust control from data via uncertainty model sets identification

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 noisy input-output measurements are available, together with some general information on the plant and on the noise characteristics. The emphasis is placed on the design of controllers guaranteeing robust stability and robust performance, and on the tradeoff between controller complexity and achievable robust performance. 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_∞ optimization techniques. This control structure is chosen because, if needed, it can be designed to be robust also in the presence of input saturation. Then, the robust performance of the designed controller is computed, allowing us to determine the level of model complexity needed to guarantee a desired closed-loop performance. A numerical example illustrates the effectiveness of the proposed design procedure