Algorithms for linear quadratic optimization:
This up-to-date reference offers valuable theoretical, algorithmic, and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems - providing an overview of recent advances in control and systems theory, numerical linear algebra, numerical optimizati...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1996
|
| Edition: | 1. printing |
| Series: | Pure and applied mathematics
200 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This up-to-date reference offers valuable theoretical, algorithmic, and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems - providing an overview of recent advances in control and systems theory, numerical linear algebra, numerical optimization, scientific computations, and software engineering Examining state-of-the-art linear algebra algorithms and associated software, Algorithms for Linear-Quadratic Optimization presents algorithms in a concise, informal language that facilitates computer implementation...discusses the mathematical description, applicability, and limitations of particular solvers...summarizes numerical comparisons of various algorithms...highlights topics of current interest, including H[subscript infinity] and H[subscript 2] optimization, defect correction, and Schur and generalized-Schur vector methods...emphasizes structure-preserving techniques...contains many worked examples based on industrial models...covers fundamental issues in control and systems theory such as regulator and estimator design, state estimation, and robust control...and more Furnishing valuable references to key sources in the literature, Algorithms for Linear-Quadratic Optimization is an incomparable reference for applied and industrial mathematicians, control engineers, computer programmers, electrical and electronics engineers, systems analysts, operations research specialists, researchers in automatic control and dynamic optimization, and graduate students in these disciplines |
| Physical Description: | VII, 366 S. |
| ISBN: | 0824796128 |
Staff View
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| 490 | 1 | |a Pure and applied mathematics |v 200 | |
| 520 | 3 | |a This up-to-date reference offers valuable theoretical, algorithmic, and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems - providing an overview of recent advances in control and systems theory, numerical linear algebra, numerical optimization, scientific computations, and software engineering | |
| 520 | |a Examining state-of-the-art linear algebra algorithms and associated software, Algorithms for Linear-Quadratic Optimization presents algorithms in a concise, informal language that facilitates computer implementation...discusses the mathematical description, applicability, and limitations of particular solvers...summarizes numerical comparisons of various algorithms...highlights topics of current interest, including H[subscript infinity] and H[subscript 2] optimization, defect correction, and Schur and generalized-Schur vector methods...emphasizes structure-preserving techniques...contains many worked examples based on industrial models...covers fundamental issues in control and systems theory such as regulator and estimator design, state estimation, and robust control...and more | ||
| 520 | |a Furnishing valuable references to key sources in the literature, Algorithms for Linear-Quadratic Optimization is an incomparable reference for applied and industrial mathematicians, control engineers, computer programmers, electrical and electronics engineers, systems analysts, operations research specialists, researchers in automatic control and dynamic optimization, and graduate students in these disciplines | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface iii
1 Linear Quadratic Optimization Problems 1
1.1 Standard Linear Quadratic Optimization Problems 2
1.1.1 Basic theory 3
1.1.2 Standard control problems 17
1.2 Problems Reducible to Standard Linear Quadratic Optimiza¬
tion Problems 20
1.2.1 Related problems and control schemes 20
1.2.2 Numerical example 27
1.3 Robust Control 36
1.3.1 Performance specification and the Hoo optimization
problem 37
1.3.2 Standard robust control problem 42
1.3.3 Hi optimal control 49
1.4 Basic Numerical Linear Algebra Algorithms and Software . 53
1.4.1 Algorithms and programs 53
1.4.2 Numerical issues 55
1.4.3 Basic algorithms 58
1.5 Overview of Algorithms 68
1.5.1 Direct iteration algorithms 70
1.5.2 Doubling algorithms 74
1.5.3 Algorithms for sequential state estimation 77
v
vi Contents
1.5.4 Defect correction 85
References 87
2 Newton Algorithms 97
2.1 Basic Theory 98
2.1.1 Newton s method 98
2.1.2 Stabilization methods 101
2.2 Computation of Real Schur Form and Invariant Subspaces . 105
2.2.1 Basic definitions and properties 105
2.2.2 Preprocessing algorithms 114
2.2.3 The QR algorithm 118
2.2.4 Real Schur form computation and ordering 135
2.3 Solving Sylvester and Lyapunov Equations 143
2.3.1 Solving Sylvester equations 144
2.3.2 Solving Lyapunov equations 159
2.3.3 Solving stable non negative definite Lyapunov equa¬
tions 162
2.4 Stabilization Algorithms 174
2.4.1 Full stabilization algorithms 174
2.4.2 Partial stabilization algorithms 177
2.5 Newton Based Riccati Solvers 179
2.5.1 Algorithmic templates 180
2.5.2 Computational issues 183
2.5.3 Applicability and limitations 186
References 191
3 Schur and Generalized Schur Algorithms 197
3.1 Basic Theory 198
3.1.1 Schur vectors method 199
3.1.2 Generalized Schur vectors method 202
3.2 Computation of Generalized Real Schur Form and Deflating
Subspaces 211
3.2.1 Basic definitions and properties 212
3.2.2 Computation of generalized real Schur form 217
3.2.3 Ordering generalized real Schur form 233
3.3 Schur Based Riccati Solvers 243
3.3.1 Algorithmic templates 243
3.3.2 Computational issues 250
3.3.3 Applicability and limitations 252
3.4 Generalized Schur Based Riccati Solvers 260
3.4.1 Algorithmic templates 260
3.4.2 Computational issues 266
Contents vii
3.4.3 Applicability and limitations 267
References 275
4 Structure Preserving Algorithms 281
4.1 Basic Theory 282
4.1.1 Matrix sign function method 283
4.1.2 Structure preserving QR type methods 287
4.1.3 Multishift method 295
4.2 Matrix Sign Function Algorithm 298
4.2.1 Algorithmic templates 298
4.2.2 Computational issues 300
4.2.3 Applicability and limitations 303
4.3 Structure Preserving QR Type Algorithms 306
4.3.1 Algorithmic templates 306
4.3.2 Computational issues 322
4.3.3 Applicability and limitations 325
4.4 Multishift Algorithm 330
4.4.1 Algorithmic templates 330
4.4.2 Computational issues 336
4.4.3 Applicability and limitations 336
References 339
Appendixes
A Comparison of Riccati Solvers 345
B Notation and Abbreviations 353
B.I Notation 353
B.2 Abbreviations 356
Index of Algorithms Definitions 357
Index 359
|
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| indexdate | 2024-07-09T18:05:33Z |
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| isbn | 0824796128 |
| language | English |
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| spelling | Sima, Vasile Verfasser aut Algorithms for linear quadratic optimization Vasile Sima 1. printing New York [u.a.] Dekker 1996 VII, 366 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 200 This up-to-date reference offers valuable theoretical, algorithmic, and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems - providing an overview of recent advances in control and systems theory, numerical linear algebra, numerical optimization, scientific computations, and software engineering Examining state-of-the-art linear algebra algorithms and associated software, Algorithms for Linear-Quadratic Optimization presents algorithms in a concise, informal language that facilitates computer implementation...discusses the mathematical description, applicability, and limitations of particular solvers...summarizes numerical comparisons of various algorithms...highlights topics of current interest, including H[subscript infinity] and H[subscript 2] optimization, defect correction, and Schur and generalized-Schur vector methods...emphasizes structure-preserving techniques...contains many worked examples based on industrial models...covers fundamental issues in control and systems theory such as regulator and estimator design, state estimation, and robust control...and more Furnishing valuable references to key sources in the literature, Algorithms for Linear-Quadratic Optimization is an incomparable reference for applied and industrial mathematicians, control engineers, computer programmers, electrical and electronics engineers, systems analysts, operations research specialists, researchers in automatic control and dynamic optimization, and graduate students in these disciplines Algoritmen gtt Controleleer gtt Lineaire systemen gtt Optimaliseren gtt Optimisation mathématique ram Control theory Mathematical optimization Linearquadratische Kontrolltheorie (DE-588)4300607-3 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Quadratische Optimierung (DE-588)4130555-3 gnd rswk-swf Linearquadratische Kontrolltheorie (DE-588)4300607-3 s Algorithmus (DE-588)4001183-5 s DE-604 Quadratische Optimierung (DE-588)4130555-3 s Lineare Optimierung (DE-588)4035816-1 s Pure and applied mathematics 200 (DE-604)BV000001885 200 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007507031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sima, Vasile Algorithms for linear quadratic optimization Pure and applied mathematics Algoritmen gtt Controleleer gtt Lineaire systemen gtt Optimaliseren gtt Optimisation mathématique ram Control theory Mathematical optimization Linearquadratische Kontrolltheorie (DE-588)4300607-3 gnd Algorithmus (DE-588)4001183-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd Quadratische Optimierung (DE-588)4130555-3 gnd |
| subject_GND | (DE-588)4300607-3 (DE-588)4001183-5 (DE-588)4035816-1 (DE-588)4130555-3 |
| title | Algorithms for linear quadratic optimization |
| title_auth | Algorithms for linear quadratic optimization |
| title_exact_search | Algorithms for linear quadratic optimization |
| title_full | Algorithms for linear quadratic optimization Vasile Sima |
| title_fullStr | Algorithms for linear quadratic optimization Vasile Sima |
| title_full_unstemmed | Algorithms for linear quadratic optimization Vasile Sima |
| title_short | Algorithms for linear quadratic optimization |
| title_sort | algorithms for linear quadratic optimization |
| topic | Algoritmen gtt Controleleer gtt Lineaire systemen gtt Optimaliseren gtt Optimisation mathématique ram Control theory Mathematical optimization Linearquadratische Kontrolltheorie (DE-588)4300607-3 gnd Algorithmus (DE-588)4001183-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd Quadratische Optimierung (DE-588)4130555-3 gnd |
| topic_facet | Algoritmen Controleleer Lineaire systemen Optimaliseren Optimisation mathématique Control theory Mathematical optimization Linearquadratische Kontrolltheorie Algorithmus Lineare Optimierung Quadratische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007507031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT simavasile algorithmsforlinearquadraticoptimization |