Closed-loop identification of uncertainty models for robust control design: a set membership approach

The paper considers the problem of identifying uncertainty model sets, defined by an approximated model of the plant to be identified and a frequency domain bound on the modeling error. It is supposed that the measurements consist of time domain samples, collected in closed loop operations and corrupted by a power bounded noise. The model is supposed to be used for robust control design, whose performance is measured by a given closed loop H_∞ norm, and the “goodness” of the model is measured by the discrepancy between the closed loop performance predicted by the model and the one actually achieved on the plant. It is shown that identifying a model minimizing this discrepancy is equivalent to finding the best approximated model of the dual Youla parametrization of the plant in a suitably weighted H_∞ norm. Then, an optimal uncertainty model is derived for the dual Youla parametrized plant, from which an uncertainty model for the actual plant is obtained. Such an uncertainty model is finally used for designing a robust controller and evaluating the closed loop performance that can be guaranteed when the designed controller is applied to the actual plant