Control of Multi-agent Systems : Theory and Simulations with Python

✍ Scribed by Masaaki Nagahara; Shun-Ichi Azuma; Hyo-Sung Ahn

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 244
• Series: Advanced Textbooks in Control and Signal Processing
• Category: Library

✦ Synopsis

This textbook teaches control theory for multi-agent systems. Readers will learn the basics of linear algebra and graph theory, which are then developed to describe and solve multi-agent control problems. The authors address important and fundamental problems including

✦ Table of Contents

Series Editor’s Foreword
Preface
Contents
Mathematical Symbols
1 Introduction
1.1 What is a Multi-agent System?
1.2 Multi-agent Systems in the Real World
1.2.1 Sensor Network
1.2.2 Systems Biology
1.2.3 Swarm Robotics
1.2.4 Collective Behaviors
1.2.5 UAVs
1.2.6 Human Society
1.3 Control of Multi-agent Systems: Emerging Topics in Systems and Control
1.3.1 Consensus Control
1.3.2 Coverage Control
1.3.3 Formation Control
1.3.4 Controllability of Networks
1.3.5 Model Predictive Control
1.3.6 Event-Triggered and Sparse Control
1.4 Multi-agent Systems in Other Important Research Fields
1.4.1 Graph Signal Processing
1.4.2 Machine Learning
1.4.3 Distributed Optimization
1.4.4 Boolean Networks
1.4.5 Swarm Intelligence
1.4.6 Synchronization
1.5 Summary
2 Linear Algebra and Graph Theory with Python
2.1 Brief Introduction to Python
2.1.1 An Overview of Python
2.1.2 Python Environment
2.1.3 Hello World
2.1.4 Numerical Computation with Python
2.2 Linear Algebra
2.2.1 Notation
2.2.2 Matrix Rank
2.2.3 Positive and Non-negative Matrices
2.2.4 Eigenvalues
2.2.5 Jordan Canonical Form and Spectral Decomposition
2.2.6 Spectral Mapping Theorem
2.2.7 Gershgorin Circle Theorem
2.2.8 Perron–Frobenius Theory
2.2.9 Definite Matrices
2.2.10 Linear Systems and Matrix Exponential
2.3 Python Codes for Linear Algebra
2.3.1 Python Code 2.1: Gershgorin Circles
2.3.2 Python Code 2.2: ODE
2.4 Graph Theory
2.4.1 What is a Graph?
2.4.2 Connectivity
2.4.3 Spanning Tree
2.4.4 Graph Laplacian
2.4.5 Perron Matrices
2.4.6 Graph Connectivity Analysis with Graph Laplacian and Perron Matrices
2.4.7 Graph-Related Dynamical Systems
2.5 Python Codes for Graph Theory
2.5.1 Python Code 2.3: Graph Drawing
2.5.2 Python Code 2.4: Directed Tree
2.5.3 Python Code 2.5: Spanning Tree
2.5.4 Python Code 2.6: Adjacency Matrix
2.5.5 Python Code 2.7: Perron Matrix of a Balanced Graph
2.5.6 Python Code 2.8: Graph Laplacian
2.6 Summary
2.7 Exercises
3 Consensus Control
3.1 Consensus Problem
3.2 Consensus Control
3.2.1 Consensus Controllers for Integrator Agents
3.2.2 Conditions for Consensus
3.3 Discrete-Time Case
3.4 Performance of Consensus Controllers
3.5 Python Codes
3.5.1 Python Code 3.1: Consensus Control in Continuous Time
3.5.2 Python Code 3.2: Consensus Control in Discrete Time
3.6 Summary
3.7 Exercises
4 Coverage Control
4.1 Coverage Problem
4.2 Voronoi Diagrams
4.2.1 Definition
4.2.2 Relation to Coverage
4.3 Coverage Control
4.3.1 Gradient Systems
4.3.2 Coverage Controllers for Integrator Agents
4.3.3 Proof of Theorem 4.1
4.4 Application to Multi-agent Display
4.5 Python Codes
4.5.1 Python Code 4.1: Computation of Voronoi Diagram and Voronoi Centroids
4.5.2 Python Code 4.2: Coverage Control
4.6 Summary
4.7 Exercises
4.8 Appendices
4.8.1 Existence of Unique Solution to Nonlinear Systems
4.8.2 LaSalle's Invariance Principle
5 Formation Control
5.1 Distributed Formation Control
5.2 Rigidity Theory
5.2.1 Distance Rigidity
5.2.2 Bearing Rigidity
5.2.3 Weak Rigidity (Angle Rigidity)
5.3 Rigidity-Induced Formation Control
5.3.1 Distance-Based Formation Control
5.3.2 Bearing-Based Formation Control
5.3.3 Angle-Based Formation Control
5.4 Python Codes
5.4.1 Python Code 5.1: Distance-Based Formation Control
5.4.2 Python Code 5.2: Bearing-Based Formation Control
5.4.3 Python Code 5.3: Angle-Based Formation Control
5.5 Summary
5.6 Exercises
6 Distributed Optimization
6.1 Convex Optimization
6.2 Group Testing
6.3 Gradient-Based Algorithms
6.3.1 Gradient Descent Algorithm
6.3.2 Gradient Projection Algorithm
6.3.3 Subgradient Methods
6.4 Proximal Algorithms
6.4.1 Proximal Operator
6.4.2 Proximal Gradient Algorithm
6.4.3 ADMM
6.5 Distributed Optimization
6.5.1 Distributed Subgradient Algorithm
6.5.2 Distributed ADMM
6.5.3 Distributed ADMM with Regularization
6.6 Python Codes
6.6.1 Python Code 6.1: Group Testing by CVXPY
6.6.2 Python Code 6.2: Group Testing by Gradient Projection
6.6.3 Python Code 6.3: Group Testing by Subgradient Method
6.6.4 Python Code 6.4: Group Testing by FISTA
6.6.5 Python Code 6.5: Group Testing by Distributed Subgradient Projection
6.6.6 Python Code 6.6: Group Testing by Distributed ADMM
6.6.7 Python Code 6.7: Group Testing by Distributed ADMM with Regularization
6.7 Summary
6.8 Exercises
7 Viral Spreading Phenomenon
7.1 Viral Spreading Phenomenon over Complex Networks
7.2 Mathematical Models of Viral Spreading Phenomenon
7.2.1 SI Model
7.2.2 SIS Model
7.2.3 SIR Model
7.3 Spreading Phenomenon over Complex Networks
7.3.1 Random Networks
7.3.2 Viral Spreading over Random Networks
7.3.3 Multi-agent Simulation of Viral Spreading
7.4 Python Codes
7.4.1 Python Code 7.1: SI Model
7.4.2 Python Code 7.2: SIS Model
7.4.3 Python Code 7.3: SIR Model
7.4.4 Python Code 7.4: Erdös–Rényi Random Graph
7.4.5 Python Code 7.5: Scale-Free Network
7.4.6 Python Code 7.6: Multi-agent Simulation over a Complex Network
7.5 Summary
7.6 Exercises
Index