Distributed Cooperative Control

Preface xii

About the Companion Website xiv

1 Introduction 1

1.1 Motivation and Challenges 1

1.1.1 From Collective Behaviors to Cooperative Control 1

1.1.2 Challenges 2

1.2 Background and Related Work 4

1.2.1 Networked Communication Systems 4

1.2.2 Cooperating Autonomous Mobile Robots 5

1.2.3 Nanoscale Systems and Laser Synchronization 7

1.3 Overview of the Book 9

References 12

2 Distributed Consensus and Consensus Filters 19

2.1 Introduction and Literature Review 19

2.2 Preliminaries on Graph Theory 22

2.3 Distributed Consensus 26

2.3.1 The Continuous-Time Consensus Protocol 26

2.3.2 The Discrete-Time Consensus Protocol 28

2.4 Distributed Consensus Filter 29

2.4.1 PI Average Consensus Filter: Continuous-Time 30

2.4.2 PI Average Consensus Filter: Discrete-Time 30

References 31

Part I Distributed Consensus for Networked Communication Systems 37

3 Average Consensus for Quantized Communication 39

3.1 Introduction 39

3.2 Problem Formulation 41

3.2.1 Average Consensus Protocol with Quantization 41

3.2.2 Problem Statement 42

3.3 Weighting Matrix Design for Average Consensus with Quantization 42

3.3.1 State Transformation 43

3.3.2 Design for Fixed and Directed Graphs 44

3.3.3 Design for Switching and Directed Graphs 52

3.4 Simulations and Performance Evaluation 54

3.4.1 Fixed and Directed Graphs 54

3.4.2 Switching and Directed Graphs 55

3.4.3 Fixed and Directed Graphs 56

3.4.4 Performance Comparison 57

3.5 Conclusion 61

Notes 61

References 62

4 Weighted Average Consensus for Cooperative Spectrum Sensing 64

4.1 Introduction 64

4.2 Problem Statement 67

4.3 Cooperative Spectrum Sensing Using Weighted Average Consensus 71

4.3.1 Weighted Average Consensus Algorithm 71

4.3.2 Fusion Convergence Performance in Terms of Detection Probability 72

4.3.3 Optimal Weight Design under AWGN Measurement Channels 73

4.3.4 Heuristic Weight Design under Rayleigh Fading Channels 75

4.4 Convergence Analysis 76

4.4.1 Fixed Communication Channels 76

4.4.2 Dynamic Communication Channels 79

4.4.3 Convergence Rate with Random Link Failures 83

4.5 Simulations and Performance Evaluation 87

4.5.1 SU Network Setup 87

4.5.2 Convergence of Weighted Average Consensus 88

4.5.3 Metrics and Methodologies 90

4.5.4 Performance Evaluation 91

4.6 Conclusion 97

Notes 97

References 97

5 Distributed Consensus Filter for Radio Environment Mapping 101

5.1 Introduction 101

5.2 Problem Formulation 103

5.2.1 System Configuration and Distributed Sensor Placement 103

5.2.2 The Model and Problem Statement 105

5.3 Distributed REM Tracking 106

5.3.1 System Matrix Estimation 107

5.3.2 Kalman-EM Filter 108

5.3.3 PI Consensus Filter for Distributed Estimation and Tracking 109

5.4 Communication and Computation Complexity 110

5.4.1 Communication Complexity 112

5.4.2 Computation Complexity 112

5.5 Simulations and Performance Evaluation 113

5.5.1 Dynamic Radio Transmitter 113

5.5.2 Stationary Radio Transmitter 116

5.5.3 Comparison with Existing Centralized Methods 116

5.6 Conclusion 118

Notes 119

References 119

Part II Distributed Cooperative Control for Multirobotic Systems 123

6 Distributed Source Seeking by Cooperative Robots 125

6.1 Introduction 125

6.2 Problem Formulation 126

6.3 Source Seeking with All-to-All Communications 127

6.3.1 Cooperative Estimation of Gradients 127

6.3.2 Control Law Design 128

6.4 Distributed Source Seeking with Limited Communications 133

6.5 Simulations 135

6.6 Experimental Validation 138

6.6.1 The Robot 138

6.6.2 The Experiment Setup 140

6.6.3 Experimental Results 141

6.7 Conclusion 144

Notes 144

References 144

7 Distributed Plume Front Tracking by Cooperative Robots 146

7.1 Introduction 146

7.2 Problem Statement 148

7.3 Plume Front Estimation and Tracking by Single Robot 150

7.3.1 State Equation of the Plume Front Dynamics 151

7.3.2 Measurement Equation and Observer Design 152

7.3.3 Estimation-Based Tracking Control 153

7.3.4 Convergence Analysis 155

7.4 Multirobot Cooperative Tracking of Plume Front 156

7.4.1 Boundary Robots 157

7.4.2 Follower Robots 157

7.4.3 Convergence Analysis 158

7.5 Simulations 160

7.5.1 Simulation Environment 160

7.5.2 Single-Robot Plume Front Tracking 161

7.5.3 Multirobot Cooperative Plume Front Tracking 161

7.6 Conclusion 164

Notes 165

References 165

Part III Distributed Cooperative Control for Multiagent Physics Systems 167

8 Friction Control of Nano-particle Array 169

8.1 Introduction 169

8.2 The Frenkel-Kontorova Model 170

8.3 Open-Loop Stability Analysis 172

8.3.1 Linear Particle Interactions 172

8.3.2 Nonlinear Particle Interactions 176

8.4 Control Problem Formulation 177

8.5 Tracking Control Design 178

8.5.1 Tracking Control of the Average System 178

8.5.2 Stability of Single Particles in the Closed-Loop System 181

8.6 Simulation Results 186

8.7 Conclusion 191

Notes 194

References 195

9 Synchronizing Coupled Semiconductor Lasers 197

9.1 Introduction 197

9.2 The Model of Coupled Semiconductor Lasers 198

9.3 Stability Properties of Decoupled Semiconductor Laser 200

9.4 Synchronization of Coupled Semiconductor Lasers 203

9.5 Simulation Examples 207

9.6 Conclusion 209

Notes 209

References 210

Appendix A Notation and Symbols 212

Appendix B Kronecker Product and Properties 213

Appendix C Quantization Schemes 214

Appendix D Finite L2 Gain 215

Appendix E Radio Signal Propagation Model 216

Index 218