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OPTIMAL AND EXACT CONTROL OF EVOLUTION EQUATIONS
by
Qian Song
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
August 2008
Copyright 2008 Qian Song
Object Description
| Title | Optimal and exact control of evolution equations |
| Author | Song, Qian |
| Author email | qsong@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2008-06-16 |
| Date submitted | 2008 |
| Restricted until | Restricted until 29 July 2010. |
| Date published | 2010-07-29 |
| Advisor (committee chair) | Lototsky, Sergey V. |
| Advisor (committee member) |
Deng, Yongheng Kukavica, Igor Mikulevicius, Remigijus Zhang, Jianfeng |
| Abstract | The objective of optimal control is to optimize (minimize or maximize) a certain performance index. The objective of exact control is to ensure that the solution takes a prescribed value at the prescribed time. This dissertation carries out a comparative analysis of these two control problems and derives several general methods of constricting exact feed-back and open-loop controls for deterministic and stochastic evolution equations. The exact feed-back control is carried out using the new notion of a driving function. Several procedures for the optimal selection of the driving function are discussed. It is proved that the driving function must develop a non-integrable singularity at the terminal time. |
| Keyword | optimal control; exact control |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m1443 |
| Contributing entity | University of Southern California |
| Rights | Song, Qian |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@dots.usc.edu |
| Filename | etd-Song-20080729 |
| Archival file | uscthesesreloadpub_Volume23/etd-Song-20080729.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@dots.usc.edu |
| Full text | OPTIMAL AND EXACT CONTROL OF EVOLUTION EQUATIONS by Qian Song A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) August 2008 Copyright 2008 Qian Song |
