CENTRODAL VORONOI TESSELLATIONS 를 이용한 REDUCED-ORDER 모델링에 기반한 BURGERS 방정식의 피드백 제어
REDUCED-ORDER-BASED FEEDBACK CONTROL OF BURGERS EQUATION USING CENTROIDAL VORONOI TESSELLATION
- 주제(키워드) centroidal Voronoi tessellation , feedback control , Burgers equation
- 주제(KDC) 410
- 주제(DDC) 510
- 발행기관 아주대학교
- 지도교수 이형천
- 발행년도 2007
- 학위수여년월 2007. 8
- 학위명 박사
- 학과 및 전공 일반대학원 수학과
- 본문언어 영어
초록/요약
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.
more목차
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
