The Computational Kleinman-Newton Method in Solving Nonlinear Nonquadratic Control Problems

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1998

Author dc:creator

• Kang, Jinghong

Chair dc:contributor.committeechair

• Russell, David L.

Committee members dc:contributor.committeemember

• Sun, Shu-Ming
• Rogers, Robert C.
• Lin, Tao
• Kim, Jong Uhn

• Nonlinear Nonquadratic Control
• Hamiltonian Function
• Adjoint Equation
• Fixed Point Theorem
• Contraction
• Interpolation

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-32398-17156

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/30435