Model validation and consistency
Antoulas, Athanasios C.
Master of Science
This thesis addresses model validation, important in robust control system modeling, for the identification method developed by Antoulas. Given a system model, the problem is to assess whether the model is consistent with the data. This work formulates the validation problem in the form of a quadratic optimization problem subject to a spherical constraint. This new, computationally tractable method allows us to find a necessary and sufficient condition on the energy of the input sequence required to invalidate a given model. Therefore, for a given energy level, not all the models can be invalidated. For fixed noise level, the set of invalidatable models decreases as the energy of the input sequence decreases. Moreover, even if infinite length measurements are taken, the set of plants which cannot be invalidated does not shrink to the true model. The true model, in addition, can never be invalidated using an input of finite energy.
Mathematics; Electronics; Electrical engineering; Mechanical engineering