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Choice of uncertainty structure in identification for robust control

Project members: S.G. Douma, P.M.J. Van den Hof

In identification for robust control an identified model has to be accompanied by a bound on its uncertainty, while the representation of this uncertainty should allow for robustness analysis and robust controller synthesis. A large number of such uncertainty descriptions is available from robust control theory, as e.g. a ($H_{\infty}$)-norm-bounded additive or multiplicative uncertainty on the plant model, a norm-bounded uncertainty on a closed-loop plant representation (e.g. its dual Youla parameter), uncertainties bounded in the gap or $\nu$-gap metric, and real parametric uncertainties. On the other hand, a range of identification techniques exists providing for uncertainty structures identified from the data, as e.g. parametrically structured (ellipsoidal) uncertainty, norm-bounded additive, non-parametric (boxed, ellipsoidal) additive in the frequency domain. Amongst such a variety of possible uncertainty structures a relevant question is what the implications are of a particular choice of structure in the identification for robust control problem.

Figure 3: Uncertainty structure and robust control.

An ultimate question to be answered would be what is, for a given purpose (robust stability/performance analyis or synthesis), the best model uncertainty structure in which to identify the model set (nominal model and uncertainty bound). And consequently, what would be the best experiment allowing for minimisation of the uncertainty.

While extensive literature exists dealing with characteristics of each uncertainty structure, answering the posed question requires a thorough comparison and a bridging of the gap between identification and robust control that goes beyond the present state of the art. This project is intended to highlight aspects in which the various uncertainty structures differ in their consequences for robust analysis and design and in their potentials to be determined on the basis of realistic experimental data.

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