Preface ........................................................ xi
Notation ....................................................... xv
PART I. 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 l-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 ll-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
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