Scholarly
    Communications Project


Document Type:Dissertation
Name:Jinghong Kang
Email address:jinghong@math.vt.edu
URN:1998/00409
Title:The Computational Kleinman-Newton Method in Solving Nonlinear Nonquadratic Control Problems
Degree:Doctor of Philosophy
Department:Mathematics
Committee Chair: David Russell
Chair's email:russell@math.vt.edu
Committee Members:Jong Kim
Tao Lin
Robert Rogers
Shu-ming Sun
Keywords:Nonlinear Nonquadratic Control, Hamiltonian Function, Adjoint Equation, Fixed Point Theorem, Contraction, Interpolation
Date of defense:April 23, 1998
Availability:Release the entire work immediately worldwide.

Abstract:

This thesis deals with non-linear non-quadratic optimal control problems in an autonomous system and a related iterative numerical method, the Kleinman-Newton method, for solving the problem. The thesis proves the local convergence of Kleinman-Newton method using the contraction mapping theorem and then describes how this Kleinman-Newton method may be used to numerically solve for the optimal control and the corresponding solution. In order to show the proof and the related numerical work, it is necessary to review some of earlier work in the beginning of Chapter 1 [Zhang], and to introduce the Kleinman-Newton method at the end of the chapter. In Chapter 2 we will demonstrate the proof. In Chapter 3 we will show the related numerical work and results.

List of Attached Files

thesis.pdf


The author grants to Virginia Tech or its agents the right to archive and display their thesis or dissertation in whole or in part in the University Libraries in all forms of media, now or hereafter known. The author retains all proprietary rights, such as patent rights. The author also retains the right to use in future works (such as articles or books) all or part of this thesis or dissertation.