博碩士論文 972201026 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:16 、訪客IP:54.211.135.32
姓名 駱易俗(Yi-Su Lo)  查詢紙本館藏   畢業系所 數學系
論文名稱 A Full Space Lagrange-Newton-Krylov Algorithm for Minimum Time Trajectory Optimization
(A Full Space Lagrange-Newton-Krylov Algorithm for Minimum Time Trajectory Optimization)
相關論文
★ 非線性塊狀高斯消去牛頓演算法在噴嘴流體的應用★ 以平行 Newton-Krylov-Schwarz 演算法解 Poisson-Boltzmann 方程式的有限元素解在膠體科學上的應用
★ 最小平方有限元素法求解對流擴散方程以及使用Bubble函數的改良★ Bifurcation Analysis of Incompressible Sudden Expansion Flows Using Parallel Computing
★ Parallel Jacobi-Davidson Algorithms and Software Developments for Polynomial Eigenvalue Problems in Quantum Dot Simulation★ An Inexact Newton Method for Drift-DiffusionModel in Semiconductor Device Simulations
★ Numerical Simulation of Three-dimensional Blood Flows in Arteries Using Domain Decomposition Based Scientific Software Packages in Parallel Computers★ A Parallel Fully Coupled Implicit Domain Decomposition Method for the Stabilized Finite Element Solution of Three-dimensional Unsteady Incompressible Navier-Stokes Equations
★ A Study for Linear Stability Analysis of Incompressible Flows on Parallel Computers★ Parallel Computation of Acoustic Eigenvalue Problems Using a Polynomial Jacobi-Davidson Method
★ Numerical Study of Algebraic Multigrid Methods for Solving Linear/Nonlinear Elliptic Problems on Sequential and Parallel Computers★ A Parallel Multilevel Semi-implicit Scheme of Fluid Modeling for Numerical Low-Temperature Plasma Simulation
★ Performance Comparison of Two PETSc-based Eigensolvers for Quadratic PDE Problems★ A Parallel Two-level Polynomial Jacobi-Davidson Algorithm for Large Sparse Dissipative Acoustic Eigenvalue Problems
★ Parallel Two-level Patient-specific Numerical Simulation of Three-dimensional Rheological Blood Flows in Branching Arteries★ A Markov Chain Multi-elimination Preconditioner for Elliptic PDE Problems on GPU
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 軌道最佳化問題的主要目的在於設計一最佳軌道,其必須滿足問題給定的特定條件,並達成某項衡量標準的最大或最小化。因為這樣的特性,這類問題通常被描述成一最佳化控制問題,也因此屬於數學上延伸自「變分法」領域並作為其應用之一的「最佳化控制理論」範疇。近來,隨著電子計算機效能的提昇,各種數值計算技術越來越廣泛地被應用在最佳化問題的求解上。其中兩種主要的方式稱為間接法和直接法,前者將最佳化控制問題轉換成雙點邊界值問題,後者則是轉換成一非線性規劃問題,然後再嘗試以各種數值方法求解。在這篇論文的工作中,我們將重心放在某一類型的直接法,並針對非線性規劃問題的求解提出一全空間 Lagrange-Newton-Krylov 演算法。這個演算法建立在全空間序列二次規劃的架構上,並結合全域化策略和產生初始值的程序。透過這個演算法的執行,我們試著求解數個最小時間軌道最佳化問題,而從其產生的數值結果中可以看出,這個演算法是可行並具有發展潛力的。
摘要(英) Trajectory optimization problem is concerned with the design of an optimal trajectory that maximizes or minimizes some measurement and satisfies prescribed conditions. Because of this characteristic, it is in general formulated as an optimal control problem and hence is related to the optimal control theory, a branch of mathematics as an application of the calculus of variations. Recently, with an improvement of computer powers, computational techniques become more widely used in solving optimal control problems. Two main approaches, namely direct and indirect methods, reformulated an optimal control problem as a boundary value problem and a nonlinear programming problem respectively and then numerical methods can be employed. In this work, we focus on a class of direct methods and purposed a full space Lagrange-Newton-Krylov algorithm for the nonlinear programming problems. This algorithm is based on the full space sequential quadratic programming framework and associated with particular globalization strategy and process to generate the initial guess. With the implementation of this algorithm, we try to solve several minimum time trajectory optimization problems and the numerical results exhibit the practicability and potentiality of this algorithm.
關鍵字(中) ★ 全空間二次序列規劃
★ 非線性規劃
★ 最佳化控制
★ 軌道最佳化
關鍵字(英) ★ nonlinear programming
★ optimal control
★ trajectory optimization
★ full space sequential quadratic programming
論文目次 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Optimal control problem and direct transcription . . . . . . . . . . . . 3
2.1 An introduction to optimal control problems . . . . . . . . . . . . . 3
2.1.1 Definition of variables . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 A baseline optimal control problem . . . . . . . . . . . . . . . . . 4
2.1.3 The other forms . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.4 Multi-phase problem . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.5 Indirect and direct methods . . . . . . . . . . . . . . . . . . . . 7
2.2 Indirect method formulation . . . . . . . . . . . . . . . . . . . . . 8
2.3 Direct transcription employing collocation method . . . . . . . . . . 10
2.3.1 Discretization and transformation for free final time phase . . . . 10
2.3.2 Numerical integration of state equations . . . . . . . . . . . . . . 11
2.3.3 Collocation methods . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.4 Resulting nonlinear programming problem . . . . . . . . . . . . . . 16
3 A full space Lagrange-Newton-Krylov algorithm for nonlinear programming 17
3.1 An introduction to parameter optimization problems . . . . . . . . . . 17
3.1.1 General equality-constrained optimization problem . . . . . . . . . 17
3.1.2 Optimality conditions . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Sequential quadratic programming . . . . . . . . . . . . . . . . . . . 21
3.2.1 Lagrange-Newton method . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.2 Concept of sequential quadratic programming . . . . . . . . . . . . 23
3.3 Step computation . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 Globalization strategy . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4.1 Merit function method . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.2 Globalization mechanism . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Generating an initial guess . . . . . . . . . . . . . . . . . . . . . 27
3.6 A full space Lagrange-Newton-Krylov algorithm . . . . . . . . . . . . 28
4 Applications: minimum time trajectory optimization . . . . . . . . . . . 30
4.1 Aircraft navigation problem . . . . . . . . . . . . . . . . . . . . . 30
4.1.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.1.2 Indirect method formulation . . . . . . . . . . . . . . . . . . . . 32
4.1.3 Direct transcribing formulation . . . . . . . . . . . . . . . . . . 35
4.2 Lunar launch problem . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.2 Indirect method formulation . . . . . . . . . . . . . . . . . . . . 38
4.2.3 Direct transcribing formulation . . . . . . . . . . . . . . . . . . 40
Satellite launch vehicle problem . . . . . . . . . . . . . . . . . . . . . 42
4.3.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3.2 Direct transcription formulation . . . . . . . . . . . . . . . . . . 46
5 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1 Grid tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1.1 Lunar launch problem . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1.2 Satellite launch vehicle problem . . . . . . . . . . . . . . . . . . 51
5.2 Typical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2.1 Aircraft navigation problem . . . . . . . . . . . . . . . . . . . . 52
5.2.2 Lunar launch problem . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2.3 Satellite launch vehicle problem . . . . . . . . . . . . . . . . . . 60
5.3 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.1 Lunar launch problem . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.2 Satellite launch vehicle problem . . . . . . . . . . . . . . . . . . 66
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
參考文獻 [1] J.T. Betts. Survey of numerical methods for trajectory optimization. Journal of guid-
ance, control, and dynamics, 21(2), 1998.
[2] M. Diehl, H.G. Bock, H. Diedam, and P.B. Wieber. Fast direct multiple shooting
algorithms for optimal robot control. Fast Motions in Biomechanics and Robotics,
pages 65–93, 2006.
[3] P.E. Gill, L.O. Jay, M.W. Leonard, L.R. Petzold, and V. Sharma. An SQP method
for the optimal control of large-scale dynamical systems. J. Comput. Appl. Math.,
120:197–213, 2000.
[4] C.R. Hargraves and SW Paris. Direct trajectory optimization using nonlinear pro-
gramming and collocation. 1:3–12, 1986.
[5] D.G. Hull. Optimal Control Theory for Applications. Springer-Verlag, 2003.
[6] J Nocedal and S.J. Wright. Numerical Optimization. Springer, 2006.
[7] E.E. Prudencio, R. Byrd, and X.C. Cai. Parallel full space SQP Lagrange-Newton-
Krylov-Schwarz algorithms for PDE-constrained optimization problems. SIAM J.
Sci. Comput., 27:1305–1328, 2006.
[8] W. Roh and Y. Kim. Trajectory optimization for a multi-stage launch vehicle using
time finite element and direct collocation methods. Eng. Optim., 34:15–32, 2002.
[9] O. von Stryk and R. Bulirsch. Direct and indirect methods for trajectory optimization.
Annals of Operations Research, 37(1):357–373, 1992.
指導教授 黃楓南(Feng-Nan Hwang) 審核日期 2012-8-1
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明