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Chapter 1 Overview 1

1.1 Introduction 1

1.2 Synchronization of Complex Dynamical Networks via Pinning 3

1.2.1 Stability Conditions for Complete Synchronization 4

1.2.2 Stability Conditions for Cluster Synchronization 5

1.2.3 Selective Strategies of Pinning Control 7

1.2.4 Controllable Regions 8

1.2.5 Control Methodologies 8

1.3 Consensus and Flocking of Multi-Agent Systems via Pinning 9

1.3.1 Single Virtual Leader Case 9

1.3.2 Multiple Virtual Leaders Case 10

1.3.3 Connectivity Maintenance 10

1.4 Conclusions and Notes 11

References 11

Chapter 2 Pinning Control for Complete Synchronization of Complex Dynamical Networks 17

2.1 Complex Network Models 17

2.1.1 ER Random Network Model 17

2.1.2 BA Scale-Free Network Model 19

2.1.3 A Directed Scale-Free Network Model 20

2.2 Stability Conditions for Complete Synchronization of Complex Dynamical Networks 20

2.2.1 Global Stability Conditions 24

2.2.2 Local Stability Conditions 25

2.3 Virtual Control of Pinned Complex Dynamical Networks 27

2.4 Selective Strategies of Pinning Control 32

2.4.1 Pinning Control Based on Node-Degree 32

2.4.2 Pinning Control Based on Control Rank 37

2.5 Conclusions and Notes 41

References 42

Chapter 3 Pinning Control for Cluster Synchronization of Complex Dynamical Networks 45

3.1 Problem Statement 45

3.2 Decentralized Adaptive Pinning Control Scheme 46

3.2.1 Algorithm Description 46

3.2.2 Main Results and Theoretical Analysis 46

3.2.3 Complete Synchronization Case 52

3.3 Simulation Study 53

3.3.1 Example 1：Three Clusters 54

3.3.2 Example 2：One Cluster 56

3.4 Conclusions and Notes 59

References 59

Chapter 4 Distributed Pinning-Controlled Second-Order Consensus of Multi-Agent Systems 61

4.1 Consensus Without Connectivity Assumptions 61

4.1.1 Problem Statement 62

4.1.2 Consensus Without a Leader 63

4.1.3 Consensus with a Leader 67

4.1.4 Simulation Study 70

4.2 Consensus with Preserved Network Connectivity 71

4.2.1 Problem Statement 72

4.2.2 Algorithm Design and Main Results 73

4.2.3 Consensus with a Virtual Leader 78

4.2.4 Simulation Study 83

4.3 Adaptive Consensus of Networked Mobile Agents with Nonlinear Dynamics 89

4.3.1 Problem Statement 90

4.3.2 Main Results 91

4.3.3 Simulation Study 96

4.4 Conclusions and Notes 99

References 99

Chapter 5 Distributed Pinning-Controlled Consensus in a Heterogeneous Influence Network 103

5.1 Backgrounds and Problem Statement 103

5.2 Consensus in a Heterogeneous Influence Network 104

5.3 Pinning Controlled Consensus in a Heterogeneous Influence Network 107

5.4 Conclusions and Notes 110

References 110

Chapter 6 Distributed Pinning-Controlled Flocking with a Virtual Leader 111

6.1 Introduction 111

6.2 Backgrounds and Problem Statement 113

6.3 Flocking with a Fraction of Informed Agents 115

6.3.1 Algorithm Description and Main Results 115

6.3.2 Cohesive Analysis 117

6.3.3 Velocity Matching Analysis 118

6.3.4 Collision Avoidance Analysis 123

6.4 Flocking with a Virtual Leader of Varying Velocity 123

6.4.1 Algorithm Description and Main Result 123

6.4.2 Theoretical Analysis 125

6.5 Simulation Study 128

6.5.1 Flocking with a Fraction of Informed Agents 128

6.5.2 Flocking with a Virtual Leader of Varying Velocity 130

6.5.3 Flocking with a Fraction of Informed Agents and a Virtual Leader of Varying Velocity 131

6.6 Conclusions and Notes 133

References 135

Chapter 7 Distributed Pinning-Controlled Flocking with Preserved Network Connectivity 137

7.1 Flocking Based only on Position Measurements 137

7.1.1 Background and Problem Statement 138

7.1.2 Fundamental Flocking Algorithm 138

7.1.3 Flocking with a Virtual Leader 143

7.1.4 Simulation Study 145

7.2 Adaptive Flocking of Multiple Agents Governed by Nonlinear Dynamics 149

7.2.1 Preliminaries and Problem Statement 150

7.2.2 Main Results 151

7.2.3 Simulation Study 156

7.3 Conclusions and Notes 158

References 159

Index 161