Robust synchronization of chaotic systems via feedback:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Lecture notes in control and information sciences
378 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XI, 198 S. graph. Darst. 24 cm |
| ISBN: | 9783540693062 9783540693079 |
Staff View
MARC
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| 245 | 1 | 0 | |a Robust synchronization of chaotic systems via feedback |c Ricardo Femat ; Gualberto Solis-Perales |
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Record in the Search Index
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| adam_text | Contents
Preface VII
1 Introduction to Chaos Control: An Interdisciplinary Problem 1
1.1 Chaos Control Is Suppression or Synchronization 1
References 4
2 Chaos Suppression with Least Prior Knowledge: Continuous Time
Feedback 7
2.1 Experimental Space in Frequency Domain 7
2.2 Laplace Domain Controllers for Chaos Suppression 14
2.2.1 The PI Controller 17
2.3 A Design Procedure for Laplace Domain Controllers with Dynamic
Estimation 24
2.4 Rationale of Chaos Stabilization Via Robust Geometrical Control 29
2.5 Suppressing Chaos in Second-Order Systems 37
2.5.1 Sketching the Stability Analysis 41
2.5.2 The Force between HTS Surface and the Levitated Magnet 44
2.6 Summary 47
References 47
3 Robust Synchronization of Chaotic Systems: A Proportional Integral
Approach 51
3.1 Chaos Synchronization Via Linear Feedback 51
3.1.1 The Feedback Control Scheme 53
3.1.2 The Chaos Synchronization as a Stabilization Problem 54
3.1.3 A PI Controller with Uncertainties Estimation 56
3.1.4 Local Stability Analysis for an Illustrative Example 58
3.1.5 Numerical Results for a Synchronization System 62
3.1.6 The Performance Index and Tuning Procedure 66
3.2 Chaos Synchronization Phenomena: A Classification 69
3.2.1 Some Synchronization Phenomena 71
3.3 Chaos-Based Signal Transmission Despite Master/Slave
Mismatches: An Experimental Test 80
3.3.1 The Chaos-Based Scheme 82
3.3.2 Experimental Setup 84
X Contents
3.4 Robust Stability Analysis of Chaos Synchronization 87
3.4.1 Chaos Synchronization Via Linear Feedback 88
3.4.2 Robust Stability Analysis of Synchronization Error 91
3.4.3 Illustrative Example 92
References 95
4 Robust Synchronization Via Geometrical Control: A General
Framework 99
4.1 Synchronization of Second-Order Driven Systems with Different
Model 99
4.1.1 Problem Statement 100
4.1.2 Synchronization Despite Unknown Master Model 102
4.1.3 Numerical Simulations 105
4.2 Adaptive Synchronization of High-Order Chaotic Systems:
A Feedback with Low Order Parameterization 106
4.2.1 Preliminaries 109
4.2.2 Synchronization against Uncertain Vector Fields 112
4.2.3 Complete Practical Synchronization of Chaotic Systems 115
4.2.4 Synchronization of an Inhomogeneous Chain of Oscillators.... 118
4.3 Chaos-Based Communication Scheme Via Robust Asymptotic
Feedback 120
4.3.1 Problem Statement 122
4.3.2 Results on Secure Communication Via Feedback 124
4.3.3 Illustrative Examples 128
References 135
5 Discrete-Time Feedback for Chaos Control
and Synchronization 139
5.1 Discrete - Time Control of Systems with Friction 139
5.1.1 Position Regulation of a Friction System 140
5.1.2 The Friction Force and Its Complexity 141
5.1.3 The Irregular Behavior of the Friction System 142
5.1.4 Stabilization of the Friction System 144
5.2 Chaos Suppression Via a Discrete-Time Controller 149
5.2.1 Chaos Control of the Second-Order Driven Oscillators 150
5.2.2 The Feedback Control without Velocity Measurements 151
5.2.3 The Discrete-Time Feedback Via Uncertainties Estimation.... 152
5.2.4 Numerical Simulations and Representative Examples 154
5.2.5 Discussion about the Chaos Control 156
5.3 Discrete-Time Chaos Control and Its Implications 156
5.3.1 A Robust Recursive Feedback Law 158
5.4 Synchronization of Chaotic Systems with Different Order 162
5.4.1 Problem Statement 163
5.4.2 The Proposed Feedback and Design Details 165
5.4.3 Reduced-Order Synchronization under Partial Knowledge 166
5.4.4 Reduced-Order Synchronization with Least Prior
Knowledge 168
Contents XI
5.4.5 Discussion of the Results 169
References 173
6 Remarks on Chaos Synchronizability and Synchronization 177
6.1 Complete Synchronizability 177
6.1.1 The Chaos Synchronization Problem 178
6.1.2 Synchronizability from Control of Chaotic Systems 179
6.1.3 Complete Synchronizability of Chaotic Systems 183
6.1.4 Illustrative Example 184
6.2 General Framework of Chaotic Synchronization 187
6.2.1 Lie-Based Geometry of Nonlinear Systems 188
6.2.2 Involutive Distributions and Flows 190
6.2.3 Computing the Synchronization Function 192
References 194
Index 197
Abbreviations 199
|
| any_adam_object | 1 |
| author | Femat, Ricardo Solis-Perales, Gualberto |
| author_facet | Femat, Ricardo Solis-Perales, Gualberto |
| author_role | aut aut |
| author_sort | Femat, Ricardo |
| author_variant | r f rf g s p gsp |
| building | Verbundindex |
| bvnumber | BV035248380 |
| classification_rvk | SI 845 |
| ctrlnum | (OCoLC)281149871 (DE-599)DNB988749785 |
| dewey-full | 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 |
| dewey-search | 515.39 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Maschinenbau / Maschinenwesen Mathematik |
| format | Book |
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| id | DE-604.BV035248380 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:29:35Z |
| institution | BVB |
| isbn | 9783540693062 9783540693079 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017054062 |
| oclc_num | 281149871 |
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| owner | DE-824 DE-83 |
| owner_facet | DE-824 DE-83 |
| physical | XI, 198 S. graph. Darst. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Femat, Ricardo Verfasser aut Robust synchronization of chaotic systems via feedback Ricardo Femat ; Gualberto Solis-Perales Berlin [u.a.] Springer 2008 XI, 198 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 378 Literaturangaben Synchronisierung (DE-588)4130847-5 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Synchronisierung (DE-588)4130847-5 s DE-604 Solis-Perales, Gualberto Verfasser aut Lecture notes in control and information sciences 378 (DE-604)BV005848579 378 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017054062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Femat, Ricardo Solis-Perales, Gualberto Robust synchronization of chaotic systems via feedback Lecture notes in control and information sciences Synchronisierung (DE-588)4130847-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4130847-5 (DE-588)4316104-2 |
| title | Robust synchronization of chaotic systems via feedback |
| title_auth | Robust synchronization of chaotic systems via feedback |
| title_exact_search | Robust synchronization of chaotic systems via feedback |
| title_full | Robust synchronization of chaotic systems via feedback Ricardo Femat ; Gualberto Solis-Perales |
| title_fullStr | Robust synchronization of chaotic systems via feedback Ricardo Femat ; Gualberto Solis-Perales |
| title_full_unstemmed | Robust synchronization of chaotic systems via feedback Ricardo Femat ; Gualberto Solis-Perales |
| title_short | Robust synchronization of chaotic systems via feedback |
| title_sort | robust synchronization of chaotic systems via feedback |
| topic | Synchronisierung (DE-588)4130847-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Synchronisierung Chaotisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017054062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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