Tatchi Ho

Publication Date

2000

Document Type

Dissertation/Thesis

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences

LCSH

Riccati equation

Abstract

This thesis is devoted to the study of the numerical methods for solving the continuous-time algebraic Riccati equation (CARE). In general, the numerical methods for the CARE can be divided in two major classes. The first class consists of methods that are based on the computation of the stable invariant subspace of the Hamiltonian matrix H. The methods in the second class approach the Riccati equation as a nonlinear algebraic equation through Newton iteration. There are many applications for the CARE. These equations arise in linear quadratic optimal-control problems and Kalman filtering problems, just to name two. We have selected eight numerical methods to describe, but we chose to compare seven methods. We have used a collection of 12 benchmark examples to compare the seven numerical methods for the CARE. Programs are written in MATLAB. The matrix sign function method has also been coded in Fortran 77 + LAPACK as well. MATLAB codes are provided in Appendix A. The codes for the CPU timing, flop counts, and Fortran 77 + LAPACK are provided in Appendix B. We have used different examples and matrix sizes to compare the accuracy of the seven algorithms. The absolute residuals, relative errors, and CPU times are reported as the results of the experiment. The results are provided in tables. A table of comparisons of different methods used in our experiment is presented at the end. It gives a guideline for practical uses of these methods based on this comparative study.

Comments

Includes bibliographical references (pages [64]-66)

Extent

v, 87 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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