On the Approximate Solution of Infinite Dimensional Linear-Quadratic Optimal Control Problem Via Semigroup Approach

number: 
1324
إنجليزية
Degree: 
Author: 
Ali Abdul-Kadhim Al-Zubaidi
Supervisor: 
Dr. Radhi Ali Zaboon
year: 
2006

 

The main focus of this thesis is to understand and develop some approximation techniques for infinite dimensional linear quadratic optimal control problem, where the governed equations is a partial differential equations.The necessary mathematical background principal of the problem have been presented and supported by useful mathematical comments.In this work, the finite approximation of infinite dimensional linear- quadratic optimal control problem has  been considered. A computational  algorithm based on some functional analysis theorems to solve such a  problem has been developed . Essential concluding remarks supported by examples to clarify the proposed algorithm is also presented and discussed. The convergence of optimal control resulted from the presented algorithm have been studied.Some lemmas and useful mathematical facts have been proved and developed to supported the proposed approach.Two different approximation schemes to approximate a linear quadratic optimal control problem governed by one dimensional convection-diffusion equation defined in equation (3.1), have been tested and illustrated step by step using the this proposed schemes. The comparison between the two schemes have also been studied and the numerical results are shown in Figures.The advantages and disadvantages of the proposed approach have been presented and studied, using convection-diffusion problem.