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
()normbounded additive or multiplicative uncertainty on
the plant
model, a normbounded uncertainty on a closedloop plant
representation (e.g. its dual Youla parameter), uncertainties
bounded in the gap or 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, normbounded additive, nonparametric (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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