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	Doctor of Philosophy
Department	Mathematics
Advisory Committee	Advisor Name Title David Russell Committee Chair Jong Kim Committee Member Robert Rogers Committee Member Shu-ming Sun Committee Member Tao Lin 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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