Award Date

8-2010

Degree Type

Thesis

Degree Name

Master of Science in Engineering (MSE)

Department

Electrical and Computer Engineering

First Committee Member

Pushkin Kachroo, Chair

Second Committee Member

Mehdi Ahmadian

Third Committee Member

Rama Venkat

Fourth Committee Member

Yahia Bagzouz

Graduate Faculty Representative

Mohammad Trabia

Number of Pages

148

Abstract

Uncertainty is present in our everyday decision making process as well as our understanding of the structure of the universe. As a result an intense and mathematically rigorous study of how uncertainty propagates in the dynamic systems present in our lives is warranted and arguably necessary. In this thesis we examine existing methods for uncertainty propagation in dynamic systems and present the results of a literature survey that justifies the development of a conservation based method of uncertainty propagation. Conservation methods are physics based and physics drives our understanding of the physical world. Thus, it makes perfect sense to formulate an understanding of uncertainty propagation in terms of one of the fundamental concepts in physics: conservation. We develop that theory for a small group of dynamic systems which are fundamental. They include ordinary differential equations, finite difference equations, differential inclusions and inequalities, stochastic differential equations, and Markov chains. The study presented considers uncertainty propagation from the initial condition where the initial condition is given as a prior distribution defined within a probability structure. This probability structure is preserved in the sense of measure. The results of this study are the first steps into a generalized theory for uncertainty propagation using conservation laws. In addition, it is hoped that the results can be used in applications such as robust control design for everything from transportation systems to financial markets.

Keywords

Conservation; Conservation of natural resources; Dynamic systems; Evolution; Information; Probability; Uncertainty; Uncertainty propagation

Disciplines

Applied Mathematics | Controls and Control Theory | Control Theory | Dynamic Systems | Electrical and Computer Engineering

Language

English


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