Analysis and design of nonlinear control systems:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIV, 545 S. Ill., graph. Darst. |
| ISBN: | 9783642115493 9787030259646 |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
1. INTRODUCTION 1
1.1 LINEAR CONTROL SYSTEMS 1
1.1.1 CONTROLLABILITY, OBSERVABILITY 3
1.1.2 INVARIANT SUBSPACES 6
1.1.3 ZEROS, POLES, OBSERVERS 8
1.1.4 NORMAL FORM AND ZERO DYNAMICS 10
1.2 NONLINEARITY VS. LINEARITY 14
1.2.1 LOCALIZATION 14
1.2.2 SINGULARITY -16
1.2.3 COMPLEX BEHAVIORS 18
1.3 SOME EXAMPLES OF NONLINEAR CONTROL SYSTEMS 20
REFERENCES 27
2. TOPOLOGICAL SPACE 29
2.1 METRIC SPACE 29
2.2 TOPOLOGICAL SPACES 34
2.3 CONTINUOUS MAPPING 39
2.4 QUOTIENT SPACES 44
REFERENCES 46
3. DIFFERENTIABLE MANIFOLD 47
3.1 STRUCTURE OF MANIFOLDS 47
3.2 FIBER BUNDLE 53
3.3 VECTOR FIELD- * ' 56
3.4 ONE PARAMETER GROUP 60
3.5 LIE ALGEBRA OF VECTOR FIELDS 62
3.6 CO-TANGENT SPACE 65
3.7 LIE DERIVATIVES 66
3.8 FROBENIUS' THEORY 70
3.9 LIE SERIES, CHOW'S THEOREM 72
3.10 TENSOR FIELD 75
3.11 RIEMANNIAN GEOMETRY 79
3.12 SYMPLECTIC GEOMETRY 85
REFERENCES 89
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000034097
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
4. ALGEBRA, LIE GROUP AND LIE ALGEBRA 91
4.1 GROUP 91
4.2 RING AND ALGEBRA 97
4.3 HOMOTOPY 100
4.4 FUNDAMENTAL GROUP 101
4.5 COVERING SPACE 109
4.6 LIE GROUP 113
4.7 LIE ALGEBRA OF LIE GROUP 115
4.8 STRUCTURE OF LIE ALGEBRA 117
REFERENCES 119
5. CONTROLLABILITY AND OBSERVABILITY 121
5.1 CONTROLLABILITY OF NONLINEAR SYSTEMS 121
5.2 OBSERVABILITY OF NONLINEAR SYSTEMS 136
5.3 KAIMAN DECOMPOSITION 140
REFERENCES *. * * 145
6. GLOBAL CONTROLLABILITY OF AFFINE CONTROL SYSTEMS 147
6.1 FROM LINEAR TO NONLINEAR SYSTEMS * : 147
6.2 A SUFFICIENT CONDITION 150
6.3 MULTI-HIERARCHY CASE 163
6.4 CODIM(^) = 1 168
REFERENCES 171
7. STABILITY AND STABILIZATION 173
7.1 STABILITY OF DYNAMIC SYSTEMS 173
7.2 STABILITY IN THE LINEAR APPROXIMATION 175
7.3 THE DIRECT METHOD OF LYAPUNOV 177
7.3.1 POSITIVE DEFINITE FUNCTIONS 177
7.3.2 CRITICAL STABILITY 179
7.3.3 INSTABILITY 180
7.3.4 ASYMPTOTIC STABILITY 180
7.3.5 TOTAL STABILITY 182
7.3.6 GLOBAL STABILITY * 182
7.4 LASALLE'S INVARIANCE PRINCIPLE * * * 183
7.5 CONVERSE THEOREMS TO LYAPUNOV'S STABILITY THEOREMS 185 7.5.1
CONVERSE THEOREMS TO LOCAL ASYMPTOTIC STABILITY 185
7.5.2 CONVERSE THEOREM TO GLOBAL ASYMPTOTIC STABILITY 187
7.6 STABILITY OF INVARIANT SET 188
7.7 INPUT-OUTPUT STABILITY 189
7.7.1 STABILITY OF INPUT-OUTPUT MAPPING 190
7.7.2 THE LUR'E PROBLEM 192
7.7.3 CONTROL LYAPUNOV FUNCTION 193
7.8 REGION OF ATTRACTION 194
REFERENCES 205
8. DECOUPLING 207
8.1 (/,G)-INVARIANT DISTRIBUTION 207
8.2 LOCAL DISTURBANCE DECOUPLING 213
8.3 CONTROLLED INVARIANT DISTRIBUTION * 218
8.4 BLOCK DECOMPOSITION 223
IMAGE 3
CONTENTS XI
8.5 FEEDBACK DECOMPOSITION 232
REFERENCES 235
9. INPUT-OUTPUT STRUCTURE 237
9.1 DECOUPLING MATRIX 237
9.2 MORGAN'S PROBLEM 240
9.3 INVERTIBILITY 243
9.4 DECOUPLING VIA DYNAMIC FEEDBACK 247
9.5 NORMAL FORM OF NONLINEAR CONTROL SYSTEMS 253
9.6 GENERALIZED NORMAL FORM 256
9.7 FLIESS FUNCTIONAL EXPANSION 264
9.8 TRACKING VIA FLIESS FUNCTIONAL EXPANSION 267
REFERENCES 277
10. LINEARIZATION OF NONLINEAR SYSTEMS * 279
10.1 POINCARE LINEARIZATION 279
10.2 LINEAR EQUIVALENCE OF NONLINEAR SYSTEMS 282
10.3 STATE FEEDBACK LINEARIZATION 287
10.4 LINEARIZATION WITH OUTPUTS 292
10.5 GLOBAL LINEARIZATION 295
10.6 NON-REGULAR FEEDBACK LINEARIZATION 306
REFERENCES 313
11 DESIGN OF CENTER MANIFOLD 315
11.1 CENTER MANIFOLD 315
11.2 STABILIZATION OF MINIMUM PHASE SYSTEMS 317
11.3 LYAPUNOV FUNCTION WITH HOMOGENEOUS DERIVATIVE 319 11.4
STABILIZATION OF SYSTEMS WITH ZERO CENTER 328
11.5 STABILIZATION OF SYSTEMS WITH OSCILLATORY CENTER 335
11.6 STABILIZATION USING GENERALIZED NORMAL FORM 341
11.7 ADVANCED DESIGN TECHNIQUES 349
REFERENCES 353
12 OUTPUT REGULATION 355
12.1 OUTPUT REGULATION OF LINEAR SYSTEMS 355
12.2 NONLINEAR LOCAL OUTPUT REGULATION 366
12.3 ROBUST LOCAL OUTPUT REGULATION 374
REFERENCES 377
13 DISSIPATIVE SYSTEMS 379
13.1 DISSIPATIVE SYSTEMS 379
13.2 PASSIVITY CONDITIONS 383
13.3 PASSIVITY-BASED CONTROL 388
13.4 LAGRANGE SYSTEMS 393
13.5 HAMILTONIAN SYSTEMS 397
REFERENCES 401
14 L2-GAIN SYNTHESIS * 403
14.1 HOO NORM AND L2-GAIN 403
14.2 AE» FEEDBACK CONTROL PROBLEM 409
14.3 L2-GAIN FEEDBACK SYNTHESIS 411
14.4 CONSTRUCTIVE DESIGN METHOD 417
14.5 APPLICATIONS 423
REFERENCES 429
IMAGE 4
XII CONTENTS
15 SWITCHED SYSTEMS 431
15.1 COMMON QUADRATIC LYAPUNOV FUNCTION 431
15.2 QUADRATIC STABILIZATION OF PLANAR SWITCHED SYSTEMS 454
15.3 CONTROLLABILITY OF SWITCHED LINEAR SYSTEMS 467
15.4 CONTROLLABILITY OF SWITCHED BILINEAR SYSTEMS 476
15.5 LASALLE'S INVARIANCE PRINCIPLE FOR SWITCHED SYSTEMS 483 15.6
CONSENSUS OF MULTI-AGENT SYSTEMS 492
15.6.1 TWO DIMENSIONAL AGENT MODEL WITH A LEADER 493
15.6.2 N DIMENSIONAL AGENT MODEL WITHOUT LEAD 495
REFERENCES 508
16 DISCONTINUOUS DYNAMICAL SYSTEMS 509
16.1 INTRODUCTION 509
16.2 FILIPPOV FRAMEWORK 510
16.2.1 FILIPPOV SOLUTION 510
16.2.2 LYAPUNOV STABILITY CRITERIA 513
16.3 FEEDBACK STABILIZATION 517
16.3.1 FEEDBACK CONTROLLER DESIGN: NOMINAL CASE 518
16.3.2 ROBUST STABILIZATION 521
16.4 DESIGN EXAMPLE OF MECHANICAL SYSTEMS 523
16.4.1 PD CONTROLLED MECHANICAL SYSTEMS 523
16.4.2 STATIONARY SET 524
16.4.3 APPLICATION EXAMPLE 528
REFERENCES 531
APPENDIX A SOME USEFUL THEOREMS 533
A.I SARD'S THEOREM 533
A.2 RANK THEOREM * 533
REFERENCES 533
APPENDIX B SEMI-TENSOR PRODUCT OF MATRICES 535
B.I A GENERALIZED MATRIX PRODUCT 535
B.2 SWAP MATRIX 537
B.3 SOME PROPERTIES OF SEMI-TENSOR PRODUCT 538
B.4 MATRIX FORM OF POLYNOMIALS 539
REFERENCES 540
INDEX 541 |
| any_adam_object | 1 |
| author | Cheng, Daizhan Hu, Xiaoming Shen, Tielong |
| author_GND | (DE-588)1011597705 (DE-588)1011601664 (DE-588)1011601745 |
| author_facet | Cheng, Daizhan Hu, Xiaoming Shen, Tielong |
| author_role | aut aut aut |
| author_sort | Cheng, Daizhan |
| author_variant | d c dc x h xh t s ts |
| building | Verbundindex |
| bvnumber | BV025603815 |
| classification_rvk | SK 880 ZQ 5224 |
| ctrlnum | (OCoLC)1184439670 (DE-599)BVBBV025603815 |
| dewey-full | 515.642 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.642 |
| dewey-search | 515.642 |
| dewey-sort | 3515.642 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| language | English |
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| spelling | Cheng, Daizhan Verfasser (DE-588)1011597705 aut Analysis and design of nonlinear control systems Daizhan Cheng ; Xiaoming Hu ; Tielong Shen Berlin [u.a.] Springer 2010 XIV, 545 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Reglerentwurf (DE-588)4177447-4 gnd rswk-swf Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd rswk-swf Systemanalyse (DE-588)4116673-5 gnd rswk-swf Nichtlineare Kontrolltheorie (DE-588)4475218-0 s Systemanalyse (DE-588)4116673-5 s Reglerentwurf (DE-588)4177447-4 s DE-604 Hu, Xiaoming Verfasser (DE-588)1011601664 aut Shen, Tielong Verfasser (DE-588)1011601745 aut Erscheint auch als Online-Ausgabe 978-3-642-11550-9 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423812&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020198983&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cheng, Daizhan Hu, Xiaoming Shen, Tielong Analysis and design of nonlinear control systems Reglerentwurf (DE-588)4177447-4 gnd Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Systemanalyse (DE-588)4116673-5 gnd |
| subject_GND | (DE-588)4177447-4 (DE-588)4475218-0 (DE-588)4116673-5 |
| title | Analysis and design of nonlinear control systems |
| title_auth | Analysis and design of nonlinear control systems |
| title_exact_search | Analysis and design of nonlinear control systems |
| title_full | Analysis and design of nonlinear control systems Daizhan Cheng ; Xiaoming Hu ; Tielong Shen |
| title_fullStr | Analysis and design of nonlinear control systems Daizhan Cheng ; Xiaoming Hu ; Tielong Shen |
| title_full_unstemmed | Analysis and design of nonlinear control systems Daizhan Cheng ; Xiaoming Hu ; Tielong Shen |
| title_short | Analysis and design of nonlinear control systems |
| title_sort | analysis and design of nonlinear control systems |
| topic | Reglerentwurf (DE-588)4177447-4 gnd Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Systemanalyse (DE-588)4116673-5 gnd |
| topic_facet | Reglerentwurf Nichtlineare Kontrolltheorie Systemanalyse |
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