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資料種別 図書

Numerical methods for optimal control problems with state constraints / Radosław Pytlak

詳細情報

タイトル Numerical methods for optimal control problems with state constraints / Radosław Pytlak
シリーズ名 Lecture notes in mathematics ; 1707
出版地(国名コード) DE
出版地Berlin
出版社Springer
出版年月日等 c1999
大きさ、容量等 xii, 215 p. : ill. ; 24 cm
注記 ISBN : 3540662146 (alk. paper)
注記 Includes bibliographical references (p. [197]-207) and index
ISBN 3540662146
ISSN 00758434
LC番号 99016712
出版年(W3CDTF) 1999
件名(キーワード) 制御理論
件名(キーワード) オプティミゼーション
件名(キーワード) 数値計算
件名(キーワード) Control theory
件名(キーワード) Mathematical optimization
件名(キーワード) Numerical analysis
NDLC M131
LCC QA3
LCC QA402.3
DDC 510 s
DDC 629.8/312
資料の種別 図書
言語(ISO639-2形式) eng : English

目次
 

  • Numerical methods for optimal control problems with state constraints
  • Contents
  • 1 Introduction 1
  • 1 The Calculus of Variations 1
  • 2 Optimal Control 5
  • 3 Numerical Methods for Optimal Control Problems 7
  • 2 Estimates on Solutions to Differential Equations and Their Approximations 13
  • 1 Linear Approximations 13
  • 2 Lagrangian, Hamiltonian and Reduced Gradients 19
  • 3 First Order Method 27
  • 1 Introduction 27
  • 2 Representation of Functional Directional Derivatives 31
  • 3 Relaxed Controls 32
  • 4 The Algorithm 34
  • 5 Convergence Properties of the Algorithm 38
  • 6 Proof of the Convergence Theorem, etc 41
  • 7 Concluding Remarks 52
  • 4 Implementation 55
  • 1 Implementable Algorithm 55
  • 1.1 Second Order Correction To the Line Search 65
  • 1.2 Resetting the Penalty Parameter 66
  • 2 Semi-Infinite Programming Problem 66
  • 3 Numerical Examples 68
  • 5 Second Order Method 81
  • 1 Introduction 81
  • 2 Function Space Algorithm 84
  • 3 Semi-Infinite Programming Method 86
  • 4 Bounding the Number of Constraints 92
  • 4.1 Some Remarks on Direction Finding Subproblems 94
  • 4.2 The Nonlinear Programming Problem 98
  • 4.3 The Watchdog Technique for Redundant Constraints 107
  • 4.4 Two-Step Superlinear Convergence 121
  • 4.5 Numerical Experiments 125
  • 5 Concluding Remarks 127
  • 6 Runge-Kutta Based Procedure for Optimal Control of Differential—Algebraic Equations 129
  • 1 Introduction 129
  • 2 The Method 133
  • 2.1 Implicit Runge-Kutta Methods 134
  • 2.2 Calculation of the Reduced Gradients 137
  • 3 Implementation of the Implicit Runge-Kutta Method 144
  • 3.1 Simplified Newton Iterations 144
  • 3.2 Stopping Criterion for the Newton Method 145
  • 3.3 Stepsize Selection 146
  • 4 Numerical Experiments 151
  • 5 Some Remarks on Integration and Optimization Accuracies 164
  • 6 Concluding Remarks 166
  • A A Primal Range-Space Method for Piecewise-Linear Quadratic Programming 169
  • A.1 Software Implementation 169
  • A.2 A Range-Space Method-Introduction 170
  • A.3 The Basic Method 171
  • A.4 Efficient Implementation 175
  • A.4.1 Adding a Bound to the Working Set 178
  • A.4.2 Deleting a Bound from the Working Set 182
  • A.4.3 Adding a Vector a to the Working Set 184
  • A.4.4 Deleting a Vector a from the Working Set 186
  • A.5 Computation of the Lagrange Multipliers 187
  • A.6 Modifications and Extensions 188
  • A.7 Numerical Experiments 191
  • References 197
  • List of Symbols 209
  • Subject Index 213
  • List of Tables
  • 4.1 Example 1, summary of results 71
  • 4.2 Example 2, summary of results 72
  • 4.3 Example 3, summary of results 73
  • 4.4 Parameters of the windshear problem 76
  • 5.1 Performance of FD Algorithm 126
  • 6.1 Runge-Kutta methods: order of convergence 136
  • 6.2 Example 1, CPU time (sec) 153
  • 6.3 Example 2, CPU time (sec) 155
  • 6.4 Example 3, CPU time (sec) 157
  • 6.5 Example 4, CPU time (sec) 157
  • 6.6 Performance of SQP algorithm 161
  • A.1 Comparison of LSSOL and PNTSOL codes on the problems (PLQP) with diagonal Hessian matrices 194
  • A.2 Comparison of LSSOL and PNTSOL codes on the problems (PLQP) with dense Hessian matrices 195
  • List of Figures
  • 4.1 Approximation of state constraint 56
  • 4.2 Example 1, optimal control and state trajectories for N = 1000 71
  • 4.3 Example 2, optimal control for N = 1000 74
  • 4.4 The windshear problem, optimal state trajectories 78
  • 4.5 The windshear problem, optimal state trajectories 79
  • 5.1 Geometry of a superlinearly convergent sequence 113
  • 6.1 Error estimates, Example 2 150
  • 6.2 Error estimates, Example 3 150
  • 6.3 Error estimates, Example 4 151
  • 6.4 Example 1, control profile 154
  • 6.5 Example 2, CO2 absorption/stripping process 155
  • 6.6 Example 2, control profiles 156
  • 6.7 Examples 3-4, distillation column 158
  • 6.8 Example 4, optimal control profiles 159
  • 6.9 Example 4, control profiles—sensitivity eqns. approach 160
  • 6.10 Example 5, PFD process 162
  • 6.11 Example 5, optimal temperature—Tin1, short horizon 164
  • 6.12 Example 5, optimal output—Tout1, comparison of sensitivity eqns. approach with our method 165

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