Doctoral Dissertations


"In this work, we study concepts in optimal control for dynamic equations on time scales, which unfies the discrete and continuous cases. After a brief introduction of dynamic equations on time scales, we will examine controllability and observability for linear systems. Then we construct and solve the linear quadratic regulator for arbitrary time scales. Here, we seek to find an optimal control that minimizes a given cost function associated with a linear system. We will find such an input under two different settings; when the final state is fixed and when it is free. Later, we extend these results to deal with linear quadratic tracking on time scales. The main contribution of this dissertation is the construction of the Kalman filter on time scales. In this setting, we seek to find an optimal estimate of a linear stochastic system whose state is corrupted by noisy measurements. Finally, we will make an argument that the linear quadratic regulator and the Kalman filter are mathematically dual to each other"--Abstract, page iv.


Bohner, Martin, 1966-

Committee Member(s)

Hall, Leon M., 1946-
Lawrence, Bonita A.
Balakrishnan, S. N.
Le, Vy Khoi


Mathematics and Statistics

Degree Name

Ph. D. in Mathematics


Missouri University of Science and Technology

Publication Date

Fall 2009


ix, 150 pages

Note about bibliography

Includes bibliographical references (pages 146-149).


© 2009 Nicholas J. Wintz, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Control theory -- Mathematical models
Difference equations
Equations, Quadratic
Kalman filtering -- Mathematical models

Thesis Number

T 9564

Print OCLC #


Electronic OCLC #


Included in

Mathematics Commons