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 AbstractThis thesis deals with non-linear non-quadratic optimalcontrol 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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