Author

James Bellon

Date of Award

4-21-2008

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Dr. Michael Stewart - Chair

Second Advisor

Dr. Marina Arav

Third Advisor

Dr. Frank Hall

Abstract

It is often desired to have control over a process or a physical system, to cause it to behave optimally. Optimal control theory deals with analyzing and finding solutions for optimal control for a system that can be represented by a set of differential equations. This thesis examines such a system in the form of a set of matrix differential equations known as a continuous linear time-invariant system. Conditions on the system, such as linearity, allow one to find an explicit closed form finite solution that can be more efficiently computed compared to other known types of solutions. This is done by optimizing a quadratic cost function. The optimization leads to solving a Riccati equation. Conditions are discussed for which solutions are possible. In particular, we will obtain a solution for a stable and controllable system. Numerical examples are given for a simple system with 2x2 matrix coefficients.

Included in

Mathematics Commons

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