| Author: | Bian, Chuanxin |
| Title: | Optimal coherent feedback control of linear quantum stochastic systems |
| Degree: | Ph.D. |
| Year: | 2013 |
| Subject: | Stochastic systems -- Mathematical models. Linear systems -- Mathematical models. Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Applied Mathematics |
| Pages: | xii, 77 leaves : ill. ; 30 cm. |
| Language: | English |
| Abstract: | The thesis is concerned with the coherent feedback control of linear quantum stochastic systems. Two topics are considered: 1. Squeezing enhancement of degenerate parametric amplifiers (DPAs) via coherent feedback control. 2. Coherent linear quadratic Gaussian (LQG) and H∞ control of linear quantum stochastic systems. For topic 1, the definition of squeezing ratio is first introduced by means of quadratures' variances. An in-depth investigation of squeezing performance of lossy DPAs is presented in the static case. A sufficient and necessary condition is proposed to guarantee the effectiveness for the scheme of feedback loop. To overcome the conservatism and achieve better squeezing performance, a coherent feedback control scheme is proposed. The problem is converted into a non-convex constrained programming, genetic algorithm (GA) and sequential quadratic programming (SQP) are applied in numerical examples to obtain the local optima. Detailed implementation procedure is also shown by using common optical instruments. For topic 2, a class of open linear quantum systems is formulated in terms of quantum stochastic differential equations (QSDEs) on a quantum probability space. Physical realizability is also reviewed which guarantees the system to be a meaningful quantum system. Then the standard quantum LQG and H∞ control problems are proposed based on the closed-loop plant-controller feedback control system. Under this framework, the mixed problem under consideration can be treated as a more general schematic which encompasses both quantum LQG control and quantum H∞ control. To solve the matrix polynomial equality constraints of physical realizability, the problem is then reformulated into a rank constrained linear matrix inequality (LMI) problem which is solved by Matlab and the toolbox therein. Simulation examples illustrate the advantages of the proposed method. |
| Rights: | All rights reserved |
| Access: | open access |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| b26526578.pdf | For All Users | 1.49 MB | Adobe PDF | View/Open |
Copyright Undertaking
As a bona fide Library user, I declare that:
- I will abide by the rules and legal ordinances governing copyright regarding the use of the Database.
- I will use the Database for the purpose of my research or private study only and not for circulation or further reproduction or any other purpose.
- I agree to indemnify and hold the University harmless from and against any loss, damage, cost, liability or expenses arising from copyright infringement or unauthorized usage.
By downloading any item(s) listed above, you acknowledge that you have read and understood the copyright undertaking as stated above, and agree to be bound by all of its terms.
Please use this identifier to cite or link to this item:
https://theses.lib.polyu.edu.hk/handle/200/7204