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CENTRODAL VORONOI TESSELLATIONS 를 이용한 REDUCED-ORDER 모델링에 기반한 BURGERS 방정식의 피드백 제어
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 이형천 | - |
| dc.contributor.author | 박광일 | - |
| dc.date.accessioned | 2018-11-08T07:38:49Z | - |
| dc.date.available | 2018-11-08T07:38:49Z | - |
| dc.date.issued | 2007-08 | - |
| dc.identifier.other | 2732 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/6351 | - |
| dc.description | 학위논문(박사)----아주대학교 일반대학원 :수학과,2007. 8 | - |
| dc.description.tableofcontents | List of Figures............................................................vii List of Tables.............................................................x Abstract.....................................................................0 Chapter 1. Introduction.................................................1 Chapter 2. Schematic Approach of CVT-based Model Reduction for Simulation...............................5 2.1. Generating Snapshots......................................5 2.2. Generating Reduced Bases with CVT.................7 2.3. Using a Reduced Basis to Solve a Simulation Problem..........................................................12 Chapter 3. Reduced-Order Distributed Feedback Control of Burgers Equations Using CVT....................15 3.1. The Model Problem........................................ 15 3.2. Feedback Control Design.................................16 3.3. Reduced Order Compensators..........................21 3.4. Numerical Results...........................................23 Chaper 4. Reduced-Order-Based Boundary Feedback Control of Burgers Equations Using CVT..........30 4.1. A Weighted CVT Algorithm for Generating Reduced Order Basis.......................................30 4.2 CVT-based Model Reduction for Burgers Equation..............................................33 4.3 Computational Experiments...............................48 4.4 Boundary Feedback Control for the Burgers Equation..........................................................67 4.5 Numerical Computations and Results.................75 4.6 Conclusion......................................................81 Bibliography...............................................................83 국문요약.....................................................................89 | - |
| dc.language.iso | eng | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | CENTRODAL VORONOI TESSELLATIONS 를 이용한 REDUCED-ORDER 모델링에 기반한 BURGERS 방정식의 피드백 제어 | - |
| dc.title.alternative | Guang-Ri Piao | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.alternativeName | Guang-Ri Piao | - |
| dc.contributor.department | 일반대학원 수학과 | - |
| dc.date.awarded | 2007. 8 | - |
| dc.description.degree | Master | - |
| dc.identifier.localId | 566892 | - |
| dc.identifier.url | http://dcoll.ajou.ac.kr:9080/dcollection/jsp/common/DcLoOrgPer.jsp?sItemId=000000002732 | - |
| dc.subject.keyword | centroidal Voronoi tessellation | - |
| dc.subject.keyword | feedback control | - |
| dc.subject.keyword | Burgers equation | - |
| dc.description.alternativeAbstract | Recently, CVT(centroidal Voronoi tessellation) is applied reduced order models for dynamical systems. In this thiesis, we have studied for distributed and boundary feedback control of Burgers equation with reduced order models based on CVT. First, review of the CVT schematic approaches to reduced-order bases are provided. In CVT-reduced order modelling, we start with a snapshot set just as is done in a POD(proper orthogonal decomposition)-based setting. Secondly, we develop the reduced-order feedback control for spatially distributed Burgers equation via CVT method. In this method, the density is taken to be uniform(constant) and we call this case as the ``CVT-uniform" algorithm. Finally, we shall introduce a new algorithm of CVT as a procedure to determine the basis elements for the approximating subspaces. In the CVT new algorithm, the focus is choice of nonuniform (variable) density and we call this case as the ``CVT-nonuniform" algorithm. We describe some numerical experiments including comparison of CVT(CVT-uniform, CVT-nonuniform)-based algorithm with numerical results obtained from FEM(finite element method) and POD-based algorithm. We apply CVT-nonuniform-based reduced-order modelling technique to a boundary feedback control problem for Burgers equation. | - |
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