This second edition of the popular text by John Betts incorporates lots of new material while maintaining the concise and focused presentation of the original edition. The book describes how sparse optimization methods can be combined with discretization techniques for differential-algebraic equations and used to solve optimal control and estimation problems. The interaction between optimization and integration is emphasized throughout the book. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Second Edition includes presentation of relevant background in nonlinear programming methods that exploit sparse matrix technology, along with description of discretization techniques for solving differential-algebraic equations and an extensive collection of example problems that demonstrate the methods. The SOCS software referenced within the book can be licensed from Boeing by readers interested in receiving the code and training materials for further investigation. Audience: This book will appeal to users of optimal control working in fields such as the aerospace industry; chemical process control; mathematical biology; robotics and multibody simulation; and electrical, mechanical, and structural engineering. It can also be a primary or supplemental text for graduate courses on optimal control methods. Contents: Preface; Chapter 1: Introduction to Nonlinear Programming; Chapter 2: Large, Sparse Nonlinear Programming; Chapter 3: Optimal Control Preliminaries; Chapter 4: The Optimal Control Problem; Chapter 5: Parameter Estimation; Chapter 6: Optimal Control Examples; Chapter 7: Advanced Applications; Chapter 8: Epilogue; Appendix: Software; Bibliography; Index
Author(s): Betts J.T.
Series: Advances in Design and Control
Edition: 2ed
Publisher: SIAM
Year: 2010
Language: English
Pages: 449
Tags: Автоматизация;Теория автоматического управления (ТАУ);Книги на иностранных языках;
Cover......Page 1
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming (Second edition)......Page 4
9780898716887......Page 5
Contents......Page 8
Preface......Page 14
1.1 Preliminaries......Page 16
1.2 Newton’s Method in One Variable......Page 17
1.3 Secant Method in One Variable......Page 19
1.4 Newton’s Method for Minimization in One Variable......Page 20
1.5 Newton’s Method in Several Variables......Page 22
1.6 Unconstrained Optimization......Page 23
1.7 Recursive Updates......Page 25
1.8 Equality-Constrained Optimization......Page 27
1.8.1 Newton’s Method......Page 30
1.9 Inequality-Constrained Optimization......Page 31
1.10 Quadratic Programming......Page 33
1.11.1 Merit Functions......Page 36
1.11.2 Line-Search Methods......Page 38
1.11.3 Trust-Region Methods......Page 40
1.11.4 Filters......Page 41
1.12 Nonlinear Programming......Page 43
1.13 An SQP Algorithm......Page 44
1.14 Interior-Point Methods......Page 45
1.15 Mathematical Program with Complementarity Conditions......Page 51
1.15.1 The Signum or Sign Operator......Page 52
1.15.3 The Maximum Value Operator......Page 53
1.15.5 Solving an MPEC......Page 54
1.16.2 Rank-Deficient Constraints......Page 55
1.16.3 Constraint Redundancy......Page 56
1.16.4 Discontinuities......Page 57
1.16.5 Scaling......Page 60
1.17 Derivative Approximation by Finite Differences......Page 61
1.17.1 Difference Estimates in Differential Equations......Page 63
2.1 Overview: Large, Sparse NLP Issues......Page 66
2.2.1 Background......Page 67
2.2.2 Sparse Hessian Using Gradient Differences......Page 68
2.3 Sparse QP Subproblem......Page 69
2.4 Merit Function......Page 71
2.5 Hessian Approximation......Page 73
2.6.1 Minimization Process......Page 75
2.7 Defective Subproblems......Page 77
2.8.1 QP Subproblem......Page 78
2.8.2 Feasible Point Strategy......Page 79
2.8.3 An Illustration......Page 80
2.9.1 Large, Sparse Test Problems......Page 82
2.9.2 Small, Dense Test Problems......Page 83
2.10.2 Sparse Least Squares......Page 85
2.10.3 Residual Hessian......Page 87
2.11.1 External Format......Page 88
2.11.2 Internal Format......Page 89
2.11.3 Definitions......Page 91
2.11.4 Logarithmic Barrier Function......Page 92
2.11.5 Computing a Search Direction......Page 94
2.11.6 Inertia Requirements for the Barrier KKT System......Page 97
2.11.7 Filter Globalization......Page 98
2.11.9 Initialization......Page 101
2.11.10 Outline of the Primary Algorithm......Page 102
2.11.11 Computational Experience......Page 103
3.2 Dynamic Systems......Page 106
3.3 Shooting Method......Page 108
3.4 Multiple Shooting Method......Page 110
3.5 Initial Value Problems......Page 112
3.6 Boundary Value Example......Page 120
3.8.1 Description......Page 123
3.8.2 NLP Considerations......Page 124
3.9.1 Simple Example......Page 126
3.9.3 External and Internal Differentiation......Page 130
3.9.4 Variational Derivatives......Page 133
4.1.1 Dynamic Constraints......Page 138
4.1.2 Algebraic Equality Constraints......Page 139
4.1.3 Singular Arcs......Page 140
4.2 Necessary Conditions for the Discrete Problem......Page 141
4.3 Direct versus Indirect Methods......Page 142
4.4 General Formulation......Page 144
4.5 Direct Transcription Formulation......Page 147
4.6.1 Background......Page 149
4.6.2 Standard Approach......Page 151
4.6.3 Discretization Separability......Page 152
4.6.4 Right-Hand-Side Sparsity (Trapezoidal)......Page 154
4.6.5 Hermite–Simpson (Compressed) (HSC)......Page 156
4.6.6 Hermite–Simpson (Separated) (HSS)......Page 158
4.6.7 K-Stage Runge–Kutta Schemes......Page 160
4.6.8 General Approach......Page 161
4.6.9 Performance Issues......Page 162
4.6.10 Performance Highlights......Page 164
4.7 Mesh Refinement......Page 167
4.7.1 Representing the Solution......Page 168
4.7.2 Estimating the Discretization Error......Page 169
4.7.3 Estimating the Order Reduction......Page 173
4.7.4 Constructing a New Mesh......Page 174
4.7.5 The Mesh-Refinement Algorithm......Page 176
4.7.6 Computational Experience......Page 178
4.8 Scaling......Page 181
4.9 Quadrature Equations......Page 183
4.10 Algebraic Variable Rate Constraints......Page 187
4.11 Estimating Adjoint Variables......Page 188
4.11.1 Quadrature Approximation......Page 190
4.11.2 Path Constraint Adjoints......Page 191
4.11.3 Differential Constraint Adjoints......Page 192
4.11.4 Numerical Comparisons......Page 193
4.12.1 High Index Partial Differential-Algebraic Equation......Page 207
4.12.2 State Vector Formulation......Page 208
4.12.4 The Indirect Approach......Page 209
4.12.5 Optimality Conditions ......Page 211
4.12.6 Computational Comparison—Direct versus Indirect......Page 214
4.12.7 Analysis of Results......Page 215
4.13 Questions of Efficiency......Page 220
4.14.1 Singular Arcs ......Page 227
4.14.2 State Constraints......Page 230
4.14.3 Discontinuous Control ......Page 231
5.2 The Parameter Estimation Problem......Page 234
5.3 Computing the Residuals......Page 237
5.4 Computing Derivatives......Page 238
5.4.1 Residuals and Sparsity......Page 239
5.4.3 Auxiliary Function Decomposition ......Page 240
5.4.4 Algebraic Variable Parameterization......Page 242
5.5 Computational Experience......Page 243
5.5.1 Reentry Trajectory Reconstruction......Page 245
5.5.2 Commercial Aircraft Rotational Dynamics Analysis......Page 248
5.6 Optimal Controlor Optimal Estimation?......Page 256
6.1 Space Shuttle Reentry Trajectory ......Page 262
6.2 Minimum Time to Climb......Page 271
6.2.1 Tabular Data......Page 272
6.2.2 Cubic Spline Interpolation......Page 273
6.2.3 Minimum Curvature Spline......Page 274
6.2.4 Numerical Solution......Page 277
6.3.1 Modified Equinoctial Coordinates......Page 280
6.3.3 Thrust Acceleration—Burn Arcs ......Page 282
6.3.5 Numerical Solution......Page 284
6.4 Two-Burn Orbit Transfer......Page 286
6.4.1 Simple Shooting Formulation......Page 288
6.4.2 Multiple Shooting Formulation ......Page 293
6.4.3 Collocation Formulation......Page 294
6.5 Hang Glider......Page 297
6.6 Abort Landing in the Presence of Windshear......Page 299
6.6.1 Dynamic Equations......Page 301
6.6.2 Objective Function......Page 303
6.6.4 Model Data......Page 304
6.6.5 Computational Results......Page 306
6.7 Space Station Attitude Control ......Page 308
6.8 Reorientation of an Asymmetric Rigid Body......Page 314
6.8.1 Computational Issues ......Page 315
6.9 Industrial Robot ......Page 319
6.10 Multibody Mechanism ......Page 325
6.11 Kinematic Chain......Page 330
6.12 Dynamic MPEC......Page 337
6.13 Free-Flying Robot ......Page 341
6.14 Kinetic Batch Reactor ......Page 346
6.15 Delta III Launch Vehicle......Page 351
6.16 A Two-Strain Tuberculosis Model......Page 360
6.17 Tumor Anti-angiogenesis......Page 363
7.1.1 Background and Motivation ......Page 368
7.1.2 Optimal Lunar Transfer Examples......Page 370
7.1.3 Equations of Motion......Page 372
7.1.4 Kepler Orbit Propagation......Page 373
7.1.6 Boundary Conditions ......Page 375
7.1.7 A Four-Step Solution Technique......Page 377
7.1.8 Solving the Subproblems ......Page 381
7.2.1 Orbital Phases......Page 387
7.2.2 Atmospheric Phases......Page 388
7.2.3 Boundary Conditions ......Page 390
7.2.4 Initial Guess ......Page 392
7.2.5 Numerical Results......Page 394
7.3 Delay Differential Equations......Page 400
7.4 In-Flight Dynamic Optimization of Wing Trailing Edge Surface Positions ......Page 411
7.4.1 Aircraft Dynamics for Drag Estimation......Page 413
7.4.2 Step1: Reference Trajectory Estimation......Page 415
7.4.3 Step 2: Aerodynamic Drag Model Approximation ......Page 416
7.4.5 Numerical Results......Page 417
8. Epilogue......Page 426
A.2 Sparse NLP with Sparse Finite Differences......Page 428
A.3 Optimal Control Using Sparse NLP......Page 429
Bibliography ......Page 432
Index ......Page 446
