Year of Award

10-11-2017

Degree Type

Thesis

Degree Name

Master of Philosophy (MPhil)

Department

Department of Mathematics.

Principal Supervisor

Kwok, Felix Wing Hong

Keywords

Control theory;Mathematical optimization;Differential equations, Parabolic;Differential equations, Partial

Language

English

Abstract

In this thesis, we consider the computational methods for linear parabolic optimal control problems. We wish to minimize the cost functional while fulfilling the parabolic partial differential equations (PDE) constraint. This type of problems arises in many fields of science and engineering. Since solving such parabolic PDE optimal control problems often lead to a demanding computational cost and time, an effective algorithm is desired. In this research, we focus on the distributed control problems. Three types of cost functional are considered: Target States problems, Tracking problems, and All-time problems. Our major contribution in this research is that we developed a preconditioner for each kind of problems, so our iterative method is accelerated. In chapter 1, we gave a brief introduction to our problems with a literature review. In chapter 2, we demonstrated how to derive the first-order optimality conditions from the parabolic optimal control problems. Afterwards, we showed how to use the shooting method along with the flexible generalized minimal residual to find the solution. In chapter 3, we offered three preconditioners to enhance our shooting method for the problems with symmetric differential operator. Next, in chapter 4, we proposed another three preconditioners to speed up our scheme for the problems with non-symmetric differential operator. Lastly, we have the conclusion and the future development in chapter 5.

Comments

Thesis submitted to the Department of Mathematics.;Principal supervisor: Dr. Kwok Wing Hong, Felix.Thesis (M.Phil.)--Hong Kong Baptist University, 2017.

Bibliography

Includes bibliographical references (pages 64-69).



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