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Graph Theoretic Methods in Multiagent Networks

Mehran Mesbahi and Magnus Egerstedt
Publisher: 
Princeton University Press
Publication Date: 
2010
Number of Pages: 
403
Format: 
Hardcover
Series: 
Princeton Series in Applied Mathematics
Price: 
59.50
ISBN: 
9780691140612
Category: 
Monograph
We do not plan to review this book.

Preface xi
Notation xv

PART 1. FOUNDATIONS 1
Chapter 1. Introduction 3
1.1 Hello, Networked World 3
1.2 Multiagent Systems 4
1.3 Information Exchange via Local Interactions 8
1.4 Graph-based Interaction Models 10
1.5 Looking Ahead 12
Chapter 2. Graph Theory 14
2.1 Graphs 14
2.2 Variations on the Theme 20
2.3 Graphs and Matrices 22
2.4 Algebraic and Spectral Graph Theory 27
2.5 Graph Symmetries 33
Chapter 3. The Agreement Protocol: Part I-The Static Case 42
3.1 Reaching Agreement: Undirected Networks 46
3.2 Reaching Agreement: Directed Networks 48
3.3 Agreement and Markov Chains 58
3.4 The Factorization Lemma 61
Chapter 4. The Agreement Protocol: Part II-Lyapunov and LaSalle 72
4.1 Agreement via Lyapunov Functions 72
4.2 Agreement over Switching Digraphs 76
4.3 Edge Agreement 77
4.4 Beyond Linearity 81
Chapter 5. Probabilistic Analysis of Networks and Protocols 90
5.1 Random Graphs 90
5.2 Agreement over Random Networks 93
5.3 Agreement in the Presence of Noise 100
5.4 Other Probabilistic Models of Networks 108

PART 2. MULTIAGENT NETWORKS 115
Chapter 6. Formation Control 117
6.1 Formation Specification: Shapes 118
6.2 Formation Specification: Relative States 123
6.3 Shape-based Control 127
6.4 Relative State-based Control 130
6.5 Dynamic Formation Selection 143
6.6 Assigning Roles 151
Chapter 7. Mobile Robots 159
7.1 Cooperative Robotics 160
7.2 Weighted Graph-based Feedback 162
7.3 Dynamic Graphs 167
7.4 Formation Control Revisited 169
7.5 The Coverage Problem 176
Chapter 8. Distributed Estimation 191
8.1 Distributed Linear Least Squares 191
8.2 Pulsed Intercluster Communication 199
8.3 Implementation over Wireless Networks 208
8.4 Distributed Kalman Filtering 212
Chapter 9. Social Networks, Epidemics, and Games 226
9.1 Diffusion on Social Networks-The Max Protocol 226
9.2 The Threshold Protocol 229
9.3 Epidemics 233
9.4 The Chip Firing Game 243

PART 3. NETWORKS AS SYSTEMS 251
Chapter 10. Agreement with Inputs and Outputs 253
10.1 The Basic Input-Output Setup 253
10.2 Graph Theoretic Controllability: The SISO Case 260
10.3 Graph Theoretic Controllability: The MIMO Case 269
10.4 Agreement Reachability 276
10.5 Network Feedback 280
10.6 Optimal Control 282
Chapter 11. Synthesis of Networks 293
11.1 Network Formation 293
11.2 Local Formation Games 294
11.3 Potential Games and Best Response Dynamics 299
11.4 Network Synthesis: A Global Perspective 305
11.5 Discrete and Greedy 309
11.6 Optimizing the Weighted Agreement 312
Chapter 12. Dynamic Graph Processes 319
12.1 State-dependent Graphs 319
12.2 Graphical Equations 323
12.3 Dynamic Graph Controllability 326
12.4 What Graphs Can Be Realized? 336
12.5 Planning over Proximity Graphs 338
Chapter 13. Higher-order Networks 344
13.1 Simplicial Complexes 344
13.2 Combinatorial Laplacians 347
13.3 Triangulations and the Rips Complex 350
13.4 The Nerve Complex 354

Appendix A. 362
A.1 Analysis 362
A.2 Matrix Theory 363
A.3 Control Theory 366
A.4 Probability 372
A.5 Optimization and Games 375
Bibliography 379
Index 399

Dummy View - NOT TO BE DELETED