Type of Document Master's Thesis Author Bellon, James URN etd-04182008-135559 Title RICCATI EQUATIONS IN OPTIMAL CONTROL THEORY Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Dr. Michael Stewart Committee Chair Dr. Frank Hall Committee Member Dr. Marina Arav Committee Member Keywords
- Matrix Equations
- Riccati Equations
- Optimal Control
Date of Defense 2008-04-16 Availability unrestricted Abstract It is often desired to have control over a process or a physical system, to cause it to behave optimally. Optimal control theory dealswith 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.
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