Citation
Smith, Roy S.R. (1990) Model validation for uncertain systems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd10252002162453
Abstract
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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.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Engineering and Applied Science 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  19 September 1989 
Author Email:  roy (AT) ece.ucsb.edu 
Record Number:  CaltechETD:etd10252002162453 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd10252002162453 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4244 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  25 Oct 2002 
Last Modified:  26 Dec 2012 03:06 
Thesis Files

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