Model Validation for Uncertain Systems

Citation

Smith, Roy S.R. (1990) Model Validation for Uncertain Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7S0Z-ZY41. https://resolver.caltech.edu/CaltechETD:etd-10252002-162453

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Modern robust control synthesis techniques aim at providing robustness with respect to uncertainty in the form of both additive noise and plant perturbations. On the other hand, most popular system identification methods assume that all uncertainty is in the form of additive noise. This has hampered the application of robust control methods to practical problems. This thesis begins to address this disparity by considering the connection between uncertain models and data. The model validation problem addressed here is this: given experimental, data and a model with both additive noise and normbounded perturbations, is it possible that the model could produce the observed inputoutput data? This question is reformulated as an optimization problem: what is the minimum norm noise required to account for the data and meet the constraint imposed by the perturbation uncertainty? The assumptions typically used for robust control analysis are introduced and shown to lead to a constant matrix problem. This problem is studied in detail, and bounds on the size of the required noise are developed. The dimensionality issues that arise in the consideration of the structured singular value ([...]) also arise here. A geometric framework is used to introduce a variation on [...]. This is extended to allow the consideration of robust control analysis problems that include input and output data. The more general problem is then used to illustrate the connection between [...] and the model validation theory. The application of the theory is illustrated by a study of a laboratory process control experiment. Typical steps in the identification of a robust control model for a physical system are discussed. It is shown, by example, how the model validation theory can be used to provide insight into the limitations of uncertain models in describing physical systems.

Thesis Files