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Sets and Constraints in the Analysis Of Uncertain Systems

Paganini, Fernando (1996) Sets and Constraints in the Analysis Of Uncertain Systems. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1996.010

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Abstract

This thesis is concerned with the analysis of dynamical systems in the presence of model uncertainty. The approach of robust control theory has been to describe uncertainty in terms of a structured set of models, and has proven successful for questions, like stability, which call for a worst-case evaluation over this set. In this respect, a first contribution of this thesis is to provide robust stability tests for the situation of combined time varying, time invariant and parametric uncertainties. The worst-case setting has not been so attractive for questions of disturbance rejection, since the resulting performance criteria (e.g., ℋ∞,) treat the disturbance as an adversary and ignore important spectral structure, usually better characterized by the theory of stochastic processes. The main contribution of this thesis is to show that the set-based methodology can indeed be extended to the modeling of white noise, by employing standard statistical tests in order to identify a typical set, and performing subsequent analysis in a worst-case setting. Particularly attractive sets are those described by quadratic signal constraints, which have proven to be very powerful for the characterization of unmodeled dynamics. The combination of white noise and unmodeled dynamics constitutes the Robust ℋ2 performance problem, which is rooted in the origins of robust control theory. By extending the scope of the quadratic constraint methodology we obtain a solution to this problem in terms of a convex condition for robustness analysis, which for the first time places it on an equal footing with the ℋ∞ performance measure. A separate contribution of this thesis is the development of a framework for analysis of uncertain systems in implicit form, in terms of equations rather than input-output maps. This formulation is motivated from first principles modeling, and provides an extension of the standard input-output robustness theory. In particular, we obtain in this way a standard form for robustness analysis problems with constraints, which also provides a common setting for robustness analysis and questions of model validation and system identification.


Item Type:Report or Paper (Technical Report)
Additional Information:My first thanks go to my advisor, John Doyle. It has become customary for anyone who has had close collaboration with John to credit him with the "big picture", and I am no exception. His main contribution to my education has been, however, that instead of providing this picture as a given and rewarding me for purely technical contributions, he encouraged me to seek a role in defining this picture; I have still a long way to go in the pursuit of this goal, but this outlook on academic research has made me grow in the direction which added the most to the intellectual resources I brought to Caltech. It has been a privilege to share much of this road with many outstanding people in the Controls group at Caltech. I particularly wish to thank Raff D'Andrea, who provided his quick "parallel" thinking and his enthusiasm to "figure it out for ACC" which pushed me forward in many key opportunities. We also shared countless mates at the lab, soccer games, and philosophical conversations in the office, which helped make my days (and nights) more enjoyable. With Geir Dullerud we cultivated our common taste for mathematics; I could always turn to him for guidance and some humor on the intricate ways of the academic world, for which I am very grateful. I also wish to thank Matt Newlin, who shared with me some of his vast knowledge, Richard Murray, who often found time for me in his impossible schedule, and Stefano Soatto, who pointed me to the Bartlett test, which turned out to give the right answer after all. Some visitors such as Munzer Dahleh and Sasha Megretski provided useful technical input at some strategic times. This thesis would not have been possible without the solid education I brought from the Universidad de la Republica in Montevideo, Uruguay. The contributors are too many to give names, but I wish to thank them all for their proud and obstinate effort to provide, against many odds, a quality of education which, I have found, should envy none in the whole world. At a more fundamental level, this thesis has been built on the foundations I received from my family. My parents, Omar and Celia, and my brothers Omi and Juanjo. helped me grow up in an environment of caring. support and intellectual stimulation. From my grandfather, Fernando Herrera Ramos. I received a little of his relentless drivee to go forward; his enduring memory is present in these pages. My wife, Malena, gave me the love. unconditional support and enthusiasm for life which carried us both through this, which is truly our joint achievement. From our greater achievement, Rafael, I received the fresh breath of Life which is infinitely richer than our best theories, and whose gratuity surpasses our most consummate efforts.
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1996.010
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1996.010
Official Citation:Paganini, Fernando (1996) Sets and Constraints in the Analysis of Uncertain Systems. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechCDSTR:1996.010]
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28115
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:05 Dec 2007
Last Modified:26 Dec 2012 14:30

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