Control and nonlinearity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2007
|
| Series: | Mathematical surveys and monographs
volume 136 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis und Index: Seiten 397-420 |
| Physical Description: | xiv, 426 Seiten Diagramme 27 cm |
| ISBN: | 0821836684 9780821836682 9780821849187 |
Staff View
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Record in the Search Index
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| adam_text | MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 136 AESUETI&R CONTROL AND
NONLINEARITY JEAN-MICHEL CORON AMERICAN MATHEMATICAL SOCIETY CONTENTS
PREFACE IX PART 1. CONTROUABILITY OF LINEAR CONTROL SYSTEMS 1 CHAPTER 1.
FINITE-DIMENSIONAL LINEAR CONTROL SYSTEMS 3 1.1. DEFINITION OF
CONTROUABILITY 3 1.2. AN INTEGRAL CRITERION FOR CONTROUABILITY 4 1.3.
KALMAN S TYPE CONDITIONS FOR CONTROUABILITY 9 1.4. THE HUBERT UNIQUENESS
METHOD 19 CHAPTER 2. LINEAR PARTIAL DIFFERENTIAL EQUATIONS 23 2.1.
TRANSPORT EQUATION 24 2.2. KORTEWEG-DE VRIES EQUATION 38 2.3. ABSTRACT
LINEAR CONTROL SYSTEMS 51 2.4. WAVE EQUATION 67 2.5. HEAT EQUATION 76
2.6. A ONE-DIMENSIONAL SCHROEDINGER EQUATION 95 2.7. SINGULAR OPTIMAL
CONTROL: A LINEAR 1-D PARABOLIC-HYPERBOLIC EXAMPLE 99 2.8.
BIBLIOGRAPHICAL COMPLEMENTS 118 PART 2. CONTROUABILITY OF NONLINEAR
CONTROL SYSTEMS 121 CHAPTER 3. CONTROUABILITY OF NONLINEAR SYSTEMS IN
FINITE DIMENSION 125 3.1. THE LINEAR TEST 126 3.2. ITERATED LIE BRACKETS
AND THE LIE ALGEBRA RANK CONDITION 129 3.3. CONTROUABILITY OF DRIFTLESS
CONTROL AFFINE SYSTEMS 134 3.4. BAD AND GOOD ITERATED LIE BRACKETS 141
3.5. GLOBAL RESULTS 150 3.6. BIBLIOGRAPHICAL COMPLEMENTS 156 CHAPTER 4.
LINEARIZED CONTROL SYSTEMS AND FIXED-POINT METHODS 159 4.1. THE LINEAR
TEST: THE REGULAER CASE 159 4.2. THE LINEAR TEST: THE CASE OF LOSS OF
DERIVATIVES 165 4.3. GLOBAL CONTROUABILITY FOR PERTURBATIONS OF LINEAR
CONTROUABLE SYSTEMS 177 CHAPTER 5. ITERATED LIE BRACKETS 181 CHAPTER 6.
RETURN METHOD 187 6.1. DESCRIPTION OF THE METHOD 187 6.2. CONTROUABILITY
OF THE EULER AND NAVIER-STOKES EQUATIONS 192 VI CONTENTS 6.3. LOCAL
CONTROLLABILITY OF A 1-D TANK CONTAINING A FLUID MODELED BY THE
SAINT-VENANT EQUATIONS 203 CHAPTER 7. QUASI-STATIC DEFORMATIONS 223 7.1.
DESCRIPTION OF THE METHOD 223 7.2. APPLICATION TO A SEMILINEAR HEAT
EQUATION 225 CHAPTER 8. POWER SERIES EXPANSION 235 8.1. DESCRIPTION OF
THE METHOD 235 8.2. APPLICATION TO A KORTEWEG-DE VRIES EQUATION 237
CHAPTER 9. PREVIOUS METHODS APPLIED TO A SCHROEDINGER EQUATION 247 9.1.
CONTROLLABILITY AND UNCONTROLLABILITY RESULTS 247 9.2. SKETCH OF THE
PROOF OF THE CONTROLLABILITY IN LARGE TIME 252 9.3. PROOF OF THE
NONLOCAL CONTROLLABILITY IN SMALL TIME 263 PART 3. STABILIZATION 271
CHAPTER 10. LINEAR CONTROL SYSTEMS IN FINITE DIMENSION AND APPLICATIONS
TO NONLINEAR CONTROL SYSTEMS 275 10.1. POLE-SHIFTING THEOREM 275 10.2.
DIRECT APPLICATIONS TO THE STABILIZATION OF FINITE-DIMENSIONAL CONTROL
SYSTEMS 279 10.3. GRAMIAN AND STABILIZATION 282 CHAPTER 11.
STABILIZATION OF NONLINEAR CONTROL SYSTEMS IN FINITE DIMENSION 287 11.1.
OBSTRUCTIONS TO STATIONARY FEEDBACK STABILIZATION 288 11.2. TIME-VARYING
FEEDBACK LAWS 295 11.3. OUTPUT FEEDBACK STABILIZATION 305 11.4.
DISCONTINUOUS FEEDBACK LAWS 311 CHAPTER 12. FEEDBACK DESIGN TOOLS 313
12.1. CONTROL LYAPUNOV FUNCTION 313 12.2. DAMPING FEEDBACK LAWS 314
12.3. HOMOGENEITY 328 12.4. AVERAGING 332 12.5. BACKSTEPPING 334 12.6.
FORWARDING 337 12.7. TRANSVERSE FUNCTIONS 340 CHAPTER 13. APPLICATIONS
TO SOME PARTIAL DIFFERENTIAL EQUATIONS 347 13.1. GRAMIAN AND RAPID
EXPONENTIAL STABILIZATION 347 13.2. STABILIZATION OF A ROTATING
BODY-BEAM WITHOUT DAMPING 351 13.3. NULL ASYMPTOTIC STABILIZABILITY OF
THE 2-D EULER CONTROL SYSTEM 356 13.4. A STRICT LYAPUNOV FUNCTION FOR
BOUNDARY CONTROL OF HYPERBOLIC SYSTEMS OF CONSERVATION LAWS 361 APPENDIX
A. ELEMENTARY RESULTS ON SEMIGROUPS OF LINEAR OPERATORS 373 APPENDIX B.
DEGREE THEORY 379 BIBLIOGRAPHY 397 CONTENTS VII LIST OF SYMBOLS 421
INDEX 423
|
| adam_txt |
MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 136 AESUETI&R CONTROL AND
NONLINEARITY JEAN-MICHEL CORON AMERICAN MATHEMATICAL SOCIETY CONTENTS
PREFACE IX PART 1. CONTROUABILITY OF LINEAR CONTROL SYSTEMS 1 CHAPTER 1.
FINITE-DIMENSIONAL LINEAR CONTROL SYSTEMS 3 1.1. DEFINITION OF
CONTROUABILITY 3 1.2. AN INTEGRAL CRITERION FOR CONTROUABILITY 4 1.3.
KALMAN'S TYPE CONDITIONS FOR CONTROUABILITY 9 1.4. THE HUBERT UNIQUENESS
METHOD 19 CHAPTER 2. LINEAR PARTIAL DIFFERENTIAL EQUATIONS 23 2.1.
TRANSPORT EQUATION 24 2.2. KORTEWEG-DE VRIES EQUATION 38 2.3. ABSTRACT
LINEAR CONTROL SYSTEMS 51 2.4. WAVE EQUATION 67 2.5. HEAT EQUATION 76
2.6. A ONE-DIMENSIONAL SCHROEDINGER EQUATION 95 2.7. SINGULAR OPTIMAL
CONTROL: A LINEAR 1-D PARABOLIC-HYPERBOLIC EXAMPLE 99 2.8.
BIBLIOGRAPHICAL COMPLEMENTS 118 PART 2. CONTROUABILITY OF NONLINEAR
CONTROL SYSTEMS 121 CHAPTER 3. CONTROUABILITY OF NONLINEAR SYSTEMS IN
FINITE DIMENSION 125 3.1. THE LINEAR TEST 126 3.2. ITERATED LIE BRACKETS
AND THE LIE ALGEBRA RANK CONDITION 129 3.3. CONTROUABILITY OF DRIFTLESS
CONTROL AFFINE SYSTEMS 134 3.4. BAD AND GOOD ITERATED LIE BRACKETS 141
3.5. GLOBAL RESULTS 150 3.6. BIBLIOGRAPHICAL COMPLEMENTS 156 CHAPTER 4.
LINEARIZED CONTROL SYSTEMS AND FIXED-POINT METHODS 159 4.1. THE LINEAR
TEST: THE REGULAER CASE 159 4.2. THE LINEAR TEST: THE CASE OF LOSS OF
DERIVATIVES 165 4.3. GLOBAL CONTROUABILITY FOR PERTURBATIONS OF LINEAR
CONTROUABLE SYSTEMS 177 CHAPTER 5. ITERATED LIE BRACKETS 181 CHAPTER 6.
RETURN METHOD 187 6.1. DESCRIPTION OF THE METHOD 187 6.2. CONTROUABILITY
OF THE EULER AND NAVIER-STOKES EQUATIONS 192 VI CONTENTS 6.3. LOCAL
CONTROLLABILITY OF A 1-D TANK CONTAINING A FLUID MODELED BY THE
SAINT-VENANT EQUATIONS 203 CHAPTER 7. QUASI-STATIC DEFORMATIONS 223 7.1.
DESCRIPTION OF THE METHOD 223 7.2. APPLICATION TO A SEMILINEAR HEAT
EQUATION 225 CHAPTER 8. POWER SERIES EXPANSION 235 8.1. DESCRIPTION OF
THE METHOD 235 8.2. APPLICATION TO A KORTEWEG-DE VRIES EQUATION 237
CHAPTER 9. PREVIOUS METHODS APPLIED TO A SCHROEDINGER EQUATION 247 9.1.
CONTROLLABILITY AND UNCONTROLLABILITY RESULTS 247 9.2. SKETCH OF THE
PROOF OF THE CONTROLLABILITY IN LARGE TIME 252 9.3. PROOF OF THE
NONLOCAL CONTROLLABILITY IN SMALL TIME 263 PART 3. STABILIZATION 271
CHAPTER 10. LINEAR CONTROL SYSTEMS IN FINITE DIMENSION AND APPLICATIONS
TO NONLINEAR CONTROL SYSTEMS 275 10.1. POLE-SHIFTING THEOREM 275 10.2.
DIRECT APPLICATIONS TO THE STABILIZATION OF FINITE-DIMENSIONAL CONTROL
SYSTEMS 279 10.3. GRAMIAN AND STABILIZATION 282 CHAPTER 11.
STABILIZATION OF NONLINEAR CONTROL SYSTEMS IN FINITE DIMENSION 287 11.1.
OBSTRUCTIONS TO STATIONARY FEEDBACK STABILIZATION 288 11.2. TIME-VARYING
FEEDBACK LAWS 295 11.3. OUTPUT FEEDBACK STABILIZATION 305 11.4.
DISCONTINUOUS FEEDBACK LAWS 311 CHAPTER 12. FEEDBACK DESIGN TOOLS 313
12.1. CONTROL LYAPUNOV FUNCTION 313 12.2. DAMPING FEEDBACK LAWS 314
12.3. HOMOGENEITY 328 12.4. AVERAGING 332 12.5. BACKSTEPPING 334 12.6.
FORWARDING 337 12.7. TRANSVERSE FUNCTIONS 340 CHAPTER 13. APPLICATIONS
TO SOME PARTIAL DIFFERENTIAL EQUATIONS 347 13.1. GRAMIAN AND RAPID
EXPONENTIAL STABILIZATION 347 13.2. STABILIZATION OF A ROTATING
BODY-BEAM WITHOUT DAMPING 351 13.3. NULL ASYMPTOTIC STABILIZABILITY OF
THE 2-D EULER CONTROL SYSTEM 356 13.4. A STRICT LYAPUNOV FUNCTION FOR
BOUNDARY CONTROL OF HYPERBOLIC SYSTEMS OF CONSERVATION LAWS 361 APPENDIX
A. ELEMENTARY RESULTS ON SEMIGROUPS OF LINEAR OPERATORS 373 APPENDIX B.
DEGREE THEORY 379 BIBLIOGRAPHY 397 CONTENTS VII LIST OF SYMBOLS 421
INDEX 423 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:11:50Z |
| indexdate | 2024-07-09T21:09:04Z |
| institution | BVB |
| isbn | 0821836684 9780821836682 9780821849187 |
| language | English |
| lccn | 2006048031 |
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| physical | xiv, 426 Seiten Diagramme 27 cm |
| publishDate | 2007 |
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| publisher | American Mathematical Society |
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| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Coron, Jean-Michel 1956- Verfasser (DE-588)14156959X aut Control and nonlinearity Jean-Michel Coron Providence, Rhode Island American Mathematical Society 2007 © 2007 xiv, 426 Seiten Diagramme 27 cm txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs volume 136 Literaturverzeichnis und Index: Seiten 397-420 Commande non linéaire Commande, Théorie de la Control theory Nonlinear control theory Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s DE-604 Nichtlineare Kontrolltheorie (DE-588)4475218-0 s Erscheint auch als Online-Ausgabe 978-1-4704-1363-7 Mathematical surveys and monographs volume 136 (DE-604)BV000018014 136 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016221798&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Coron, Jean-Michel 1956- Control and nonlinearity Mathematical surveys and monographs Commande non linéaire Commande, Théorie de la Control theory Nonlinear control theory Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4475218-0 (DE-588)4032317-1 |
| title | Control and nonlinearity |
| title_auth | Control and nonlinearity |
| title_exact_search | Control and nonlinearity |
| title_exact_search_txtP | Control and nonlinearity |
| title_full | Control and nonlinearity Jean-Michel Coron |
| title_fullStr | Control and nonlinearity Jean-Michel Coron |
| title_full_unstemmed | Control and nonlinearity Jean-Michel Coron |
| title_short | Control and nonlinearity |
| title_sort | control and nonlinearity |
| topic | Commande non linéaire Commande, Théorie de la Control theory Nonlinear control theory Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Commande non linéaire Commande, Théorie de la Control theory Nonlinear control theory Nichtlineare Kontrolltheorie Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016221798&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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