Mesbahi / Egerstedt Graph Theoretic Methods in Multiagent Networks

Course Book
ISBN: 978-1-4008-3535-5
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 424 Seiten

Reihe: Princeton Series in Applied Mathematics

This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems.

The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.

The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.

This book has been adopted as a textbook at the following universities:

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- University of Stuttgart, Germany

- Royal Institute of Technology, Sweden

- Johannes Kepler University, Austria

- Georgia Tech, USA

- University of Washington, USA

- Ohio University, USA

Autoren/Hrsg.

Mesbahi, Mehran

Egerstedt, Magnus

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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

Über Autor(innen)

Mehran Mesbahi is associate professor of aeronautics and astronautics at the University of Washington. Magnus Egerstedt is associate professor of electrical and computer engineering at Georgia Institute of Technology.