Model validation for robust control

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 the validity of a model can be tested 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 v-gap metric. Recent results in the v-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. Keywords: model validation, robust control, H-infinity, nu-gap metric, flight test data, flexible beam