Title page for ETD etd-32398-17156


Type of Document Dissertation
Author Kang, Jinghong
Author's Email Address jinghong@math.vt.edu
URN etd-32398-17156
Title The Computational Kleinman-Newton Method in Solving Nonlinear Nonquadratic Control Problems
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Russell, David L. Committee Chair
Kim, Jong Uhn Committee Member
Lin, Tao Committee Member
Rogers, Robert C. Committee Member
Sun, Shu-Ming Committee Member
Keywords
  • Nonlinear Nonquadratic Control
  • Hamiltonian Function
  • Adjoint Equation
  • Fixed Point Theorem
  • Contraction
  • Interpolation
Date of Defense 1998-04-23
Availability unrestricted
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.

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