Introduction to control of oscillations and chaos:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1998
|
| Series: | [World scientific series on nonlinear science / A]
35 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 391 S. graph. Darst. |
| ISBN: | 9810230699 |
Staff View
MARC
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| 100 | 1 | |a Fradkov, Aleksandr L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to control of oscillations and chaos |c A. L. Fradkov ; A. Yu. Pogromsky |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1998 | |
| 300 | |a XIV, 391 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a [World scientific series on nonlinear science / A] |v 35 | |
| 650 | 7 | |a Chaos |2 gtt | |
| 650 | 7 | |a Comportamento caótico nos sistemas |2 larpcal | |
| 650 | 7 | |a Controle adaptativo |2 larpcal | |
| 650 | 7 | |a Controleleer |2 gtt | |
| 650 | 7 | |a Trillingen |2 gtt | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 4 | |a Nonlinear control theory | |
| 650 | 0 | 7 | |a Chaotisches System |0 (DE-588)4316104-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Chaotisches System |0 (DE-588)4316104-2 |D s |
| 689 | 0 | 2 | |a Nichtlineare Regelung |0 (DE-588)4132964-8 |D s |
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Record in the Search Index
| _version_ | 1804127142236127232 |
|---|---|
| adam_text | IMAGE 1
N
WORLD SCIENTIFIC SERIES ON *» % -. . -
ONLINEAR SCIENCE % S E R , ES A
SERIES EDITOR: LEON 0. CHUA
ITRODIICTION10 CONTROL OF
OSCILLHTIONS HNO CHAOS
A. L. FRADKOV A. YU. POGROMSKY RUSSIAN ACADEMY OF SCIENCES
^FT|G WORLD SCIENTIFIC WB SINGAPORE NEWJERSEY L SINGAPORE*
NEWJERSEYLONDON »HONGKONG
IMAGE 2
CONTENTS
PREFACE V
NOTATIONS AND DEFINITIONS 1
CHAPTER 1 INTRODUCTION 5
1.1 WHAT IS CONTROL? 5
1.1.1 MODELS OF THE CONTROLLED PLANTS 6
1.1.2 CONTROL GOALS 8
1.1.3 NAIVE CONTROL 10
1.1.4 FEEDBACK 12
1.1.5 UNCERTAINTY 13
1.1.6 NONLINEARITY 15
1.2 WHAT IS CHAOS? 18
1.3 WHAT USE IS IT? 21
1.3.1 MECHANICS AND MECHANICAL ENGINEERING 21
1.3.2 ELECTRICAL ENGINEERING AND TELECOMMUNICATIONS 22
1.3.3 CHEMISTRY AND CHEMICAL ENGINEERING 24
1.3.4 BIOLOGY, BIOCHEMISTRY AND MEDICINE 26
1.3.5 ECONOMICS AND FINANCE 27
CHAPTER 2 THE MATHEMATICS OF NONLINEAR CONTROL 29
2.1 MATHEMATICAL MODEIS OF CONTROLLED SYSTEMS 29
2.2 STABILITY AND BOUNDEDNESS 37
2.2.1 STATE-SPACE STABILITY 37
2.2.2 STABILITY THEOREMS AND LYAPUNOV FUNCTIONS 43
2.2.3 ABSOLUTE STABILITY 53
XI
IMAGE 3
XII CONTENTS
2.3 FEEDBACK LINEARIZATION AND NORMAL FORMS 61
2.4 FEEDBACK STABILIZATION AND PASSIVITY 67
2.4.1 INTRODUCTORY COMMENTS 67
2.4.2 PASSIVITY AND DISSIPATIVITY 69
2.4.3 PASSIFICATION AS A CONTROL DESIGN PROBLEM 78
2.4.4 INPUT-TO-STATE STABILITY 83
2.5 SPEED GRADIENT ALGORITHMS 87
2.5.1 GOAL-ORIENTED FORMULATION OF THE CONTROL PROBLEM . . .. 87
2.5.2 DESIGN OF SPEED GRADIENT ALGORITHMS 90
2.5.3 PROPERTIES OF THE SPEED GRADIENT ALGORITHMS 94
2.5.4 IDENTIFYING PROPERTIES OF SG ALGORITHMS 110
2.6 ROBUSTNESS OF SPEED GRADIENT ALGORITHMS WITH RESPECT TO DISTURBANCES
112
2.7 GRADIENT CONTROL OF DISCRETE-TIME SYSTEMS 116
CHAPTER 3 THE MATHEMATICS OF OSCILLATIONS AND CHAOS 121
3.1 WHAT IS OSCILLATION? 121
3.1.1 GENERAL CONCEPTS 121
3.1.2 OSCILLATIONS IN DYNAMICAL SYSTEMS 125
3.2 STABILITY OF OSCILLATIONS 132
3.2.1 CONVERGENCE AND SYNCHRONIZATION 132
3.2.2 LYAPUNOV STABILITY, LYAPUNOV EXPONENTS, BOL EXPONENTS 139 3.2.3
COMPUTATION OF THE BOL EXPONENTS 144
3.2.4 ORBITAL STABILITY 145
3.3 POINCARE MAPS 149
3.3.1 DEFINITION AND PROPERTIES OF THE POINCARE MAP 149
3.3.2 CONTROLLED POINCARE MAPS 151
3.3.3 CONTROLLED CLOSING LEMMA 156
3.4 WHAT IS CHAOS? (CONTINUED) 158
CHAPTER 4 METHODS OF NONLINEAR AND ADAPTIVE CONTROL OF OSCILLATIONS 163
4.1 ADAPTIVE CONTROL PROBLEM STATEMENT 163
4.2 DIRECT AND IDENTIFICATION APPROACHES TO ADAPTIVE CONTROL DESIGN 169
4.3 ADAPTIVE SYSTEMS WITH REFERENCE MODEIS 173
4.3.1 PROBLEM STATEMENT 173
4.3.2. STATE FEEDBACK 174
4.3.3 OUTPUT FEEDBACK 182
IMAGE 4
CONTENTS XIII
4.4 CONTROLLED SYNCHRONIZATION OF DYNAMICAL SYSTEMS 186
4.5 DECOMPOSITION BASED SYNCHRONIZATION 189
4.6 PASSIVITY BASED SYNCHRONIZATION 193
4.6.1 SEMIPASSIVITY AND -DISSIPATIVITY 193
4.6.2 SYNCHRONIZATION OF TWO LINEARLY COUPLED SYSTEMS . . .. 196
4.6.3 SYNCHRONIZATION OF SEVERAL SYSTEMS WITH MULTIPLE INTERCONNECTIONS
203
4.6.4 ADAPTIVE SYNCHRONIZATION 207
4.6.5 ADAPTIVE SYNCHRONIZATION OF UNCERTAIN SEMIPASSIVE SYSTEMS 210
4.6.6 ADAPTIVE SYNCHRONIZATION OF HYPER-MINIMUM-PHASE SYSTEMS 215
4.7 ADAPTIVE SUPPRESSION OF FORCED OSCILLATIONS 218
4.8 CONTROL OF CASCADED SYSTEMS. RELAXATION OF THE MATCHING CONDITION
232
4.8.1 INTEGRATOR BACKSTEPPING 232
4.8.2 ADAPTIVE CONTROL OF UNMATCHED SYSTEMS 238
4.9 SPEED GRADIENT CONTROL OF HAMILTONIAN SYSTEMS 247
4.9.1 CONTROL OF ENERGY 247
4.9.2 THE SWINGING (SMALL CONTROL) PROPERTY 252
4.9.3 CONTROL OF FIRST INTEGRALS 253
4.9.4 CONTROL OF GENERALIZED HAMILTONIAN SYSTEMS 257
4.10 DISCRETE ADAPTIVE CONTROL VIA LINEARIZATION OF POINCARE MAP . . 260
4.10.1 BACKGROUND AND MOTIVATION 260
4.10.2 LINEARIZATION OF THE CONTROLLED POINCARE MAP 261
4.11 CONTROL OF BIFURCATIONS 269
CHAPTER 5 CONTROL OF OSCILLATORY AND CHAOTIC SYSTEMS 273
5.1 CONTROL OF PENDULUMS 273
5.1.1 SWINGING A SIMPLE PENDULUM 273
5.1.2 PENDULUM WITH A CONTROLLED SUSPENSION POINT 280
5.2 STABILIZATION OF THE EQUILIBRIUM.POINT OF THE THERMAL CONVECTION
LOOP MODEL 286
5.3 ADAPTIVE SYNCHRONIZATION OF TWO FORCED DUFNNG S SYSTEMS . . . 295
5.4 ADAPTIVE SYNCHRONIZATION OF CHUA S CIRCUITS 304
5.5 GRADIENT CONTROL OF THE HENON SYSTEM 309
5.5.1 STABILIZING THE UNSTABLE EQUILIBRIUM OF THE HENON SYSTEM 310
IMAGE 5
XIV CONTENTS
5.5.2 SYNCHRONIZING TWO IDENTICAL HENON SYSTEMS 312
5.5.3 ADAPTIVE MODEL REFERENCE CONTROL OF THE HENON SYSTEM . 313 5.6
CONTROL OF PERIODIC AND CHAOTIC OSCILLATIONS IN THE BRUSSELLATOR MODEL
314
CHAPTER 6 APPLICATIONS 323
6.1 HOW TO TOW A CAR OUT OF A DITCH 323
6.2 SYNCHRONIZATION OF GENERATORS BASED ON TUNNEL DIODES 327
6.3 STABILIZATION OF SWINGS IN POWER SYSTEMS 333
6.4 ADAPTIVE CONTROL OF THE THIN FILM GROWTH FROM A MULTICOMPONENT GAS
342
6.5 CONTROL OF OSCILLATORY BEHAVIOR OF POPULATIONS 346
6.6 CONTROL OF A NONLINEAR BUSINESS-CYCLE MODEL 351
CHAPTER 7 CONCLUSIONS: W H AT IS THE MESSAGE OF THE BOOK? 359
EXERCISES 363
BIBLIOGRAPHY 367
INDEX 389
|
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| indexdate | 2024-07-09T18:28:39Z |
| institution | BVB |
| isbn | 9810230699 |
| language | English |
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| physical | XIV, 391 S. graph. Darst. |
| publishDate | 1998 |
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| series2 | [World scientific series on nonlinear science / A] |
| spelling | Fradkov, Aleksandr L. Verfasser aut Introduction to control of oscillations and chaos A. L. Fradkov ; A. Yu. Pogromsky Singapore [u.a.] World Scientific 1998 XIV, 391 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [World scientific series on nonlinear science / A] 35 Chaos gtt Comportamento caótico nos sistemas larpcal Controle adaptativo larpcal Controleleer gtt Trillingen gtt Chaotic behavior in systems Nonlinear control theory Chaotisches System (DE-588)4316104-2 gnd rswk-swf Nichtlineare Schwingung (DE-588)4042100-4 gnd rswk-swf Nichtlineare Regelung (DE-588)4132964-8 gnd rswk-swf Nichtlineare Schwingung (DE-588)4042100-4 s Chaotisches System (DE-588)4316104-2 s Nichtlineare Regelung (DE-588)4132964-8 s DE-604 Pogromsky, Alexander Yu. Verfasser aut A] [World scientific series on nonlinear science 35 (DE-604)BV009051753 35 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008483953&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fradkov, Aleksandr L. Pogromsky, Alexander Yu Introduction to control of oscillations and chaos Chaos gtt Comportamento caótico nos sistemas larpcal Controle adaptativo larpcal Controleleer gtt Trillingen gtt Chaotic behavior in systems Nonlinear control theory Chaotisches System (DE-588)4316104-2 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd Nichtlineare Regelung (DE-588)4132964-8 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4042100-4 (DE-588)4132964-8 |
| title | Introduction to control of oscillations and chaos |
| title_auth | Introduction to control of oscillations and chaos |
| title_exact_search | Introduction to control of oscillations and chaos |
| title_full | Introduction to control of oscillations and chaos A. L. Fradkov ; A. Yu. Pogromsky |
| title_fullStr | Introduction to control of oscillations and chaos A. L. Fradkov ; A. Yu. Pogromsky |
| title_full_unstemmed | Introduction to control of oscillations and chaos A. L. Fradkov ; A. Yu. Pogromsky |
| title_short | Introduction to control of oscillations and chaos |
| title_sort | introduction to control of oscillations and chaos |
| topic | Chaos gtt Comportamento caótico nos sistemas larpcal Controle adaptativo larpcal Controleleer gtt Trillingen gtt Chaotic behavior in systems Nonlinear control theory Chaotisches System (DE-588)4316104-2 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd Nichtlineare Regelung (DE-588)4132964-8 gnd |
| topic_facet | Chaos Comportamento caótico nos sistemas Controle adaptativo Controleleer Trillingen Chaotic behavior in systems Nonlinear control theory Chaotisches System Nichtlineare Schwingung Nichtlineare Regelung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008483953&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009051753 |
| work_keys_str_mv | AT fradkovaleksandrl introductiontocontrolofoscillationsandchaos AT pogromskyalexanderyu introductiontocontrolofoscillationsandchaos |