Model validation for robust control
Rob Davis
Abstract
This thesis is concerned with validation of the models used for robust
control. Theory is developed for validating the models used for
robust control design and applied to data from a flexible beam
and Harrier VSTOL aircraft.
Results from Caratheodory-Fejer interpolation theory are used
to extend published results to a general class of models used for
robust control. The computational tractability of these results is
then examined using techniques from computational complexity. A large
class of model validation problems are proved to be NP-hard, which
means they are computationally at least as hard as a class of problems
that are recognised to be computationally demanding. Conditions are
also obtained for when model validation can be accomplished by solving
a convex feasibility problem.
Two sets of models, that are equivalent for robust control, are shown
to be different for the purposes of validation. This is shown to be a
consequence of the difference between certain balls defined in the gap
metric. A study of the gap metric provides an interesting
interpretation of model validation and motivates the validation of
models defined as balls in the nu-gap metric. Recent results in the
nu-gap metric are used to prove validation results for the largest
set of models that are stabilizable by a certain set of robust
controllers. These may be considered as the best possible validation
results for a certain set of robust controllers.
The theoretical results are used to test the validity of models of a
flexible beam and Harrier aircraft.
It is shown that a model of the flexible beam cannot account for the
observed data, but that a modified model can. Linear models of the
Harrier are validated using data simulated by a nonlinear model. The
same linear models are also validated using flight test data from the
aircraft.