This book investigates the disagreement behavior analysis problems for signed networks in the presence of both cooperative and antagonistic interactions among agents. Owing to the existing antagonistic interactions, signed networks exhibit a variety of disagreement behaviors subject to different topology conditions, especially in comparison with commonly considered unsigned networks involving only cooperative interactions among agents. Since signed networks are generally adopted to describe the dynamics of some practical network systems, they have attracted much attention in many areas, such as biology, sociology, economics, and politics. By focusing on agents with the first-order linear dynamics, the book establishes the systematic behavior analysis frameworks for signed networks, under which diverse disagreement behaviors have been disclosed, including both convergence and fluctuation behaviors, regardless of static or dynamic network topologies. In particular, a class of dynamic signed networks has been introduced, together with the associated dynamic distributed controller design and disagreement behavior analysis of agents. This book is intended for undergraduate and graduate students, engineers, and researchers who are interested in control of network systems, multi-agent systems, social networks, and so on.
Author(s): Deyuan Meng, Mingjun Du, Yuxin Wu
Series: Intelligent Control and Learning Systems, 5
Publisher: Springer
Year: 2023
Language: English
Pages: 260
City: Singapore
Preface
Contents
1 Overview of Signed Networks
1.1 Introduction to Signed Networks
1.2 Network Disagreement Behaviors
1.3 Monograph Structure
1.4 Summary
References
2 Preliminaries
2.1 Notations
2.2 Static Signed Digraphs
2.2.1 Fixed Signed Digraphs
2.2.2 Time-Varying Signed Digraphs
2.2.3 Structural Balance Theory
2.3 Specific Matrices
2.3.1 M-Matrix
2.3.2 State Transition Matrix
2.4 Summary
References
Part I Fixed Topologies
3 Bipartite Consensus
3.1 Problem Statement
3.2 Stability of Laplacian Matrices
3.3 Bipartite Consensus
3.4 Simulation Results
3.5 Summary
References
4 Interval Bipartite Consensus
4.1 Problem Statement
4.1.1 A Motivating Example
4.1.2 Interval Bipartite Consensus
4.2 Stability of Laplacian Matrices
4.2.1 Rooted Cycle and Its Properties
4.2.2 Properties of Laplacian Matrices
4.3 Disagreement Behavior Analysis
4.4 Simulation Results
4.5 Summary
References
5 Bipartite Containment Tracking
5.1 Problem Statement
5.2 Properties of Laplacian Matrices
5.3 Disagreement Behavior Analysis
5.4 Simulation Results
5.5 Summary
References
6 Local Disagreement Characterization
6.1 Extended Structural Balance Theory
6.2 Local Disagreement Behavior Analysis
6.2.1 General Disagreement Behaviors
6.2.2 Specific Disagreement Behaviors
6.3 Simulation Results
6.4 Summary
References
Part II Switching Topologies
7 Uniform Convergence Behaviors
7.1 Problem Statement
7.2 Connection of Signed and Unsigned Networks
7.3 Uniform Convergence Results
7.3.1 Laplacian-Dependent Conditions
7.3.2 Structure-Dependent Conditions
7.4 Simulation Results
7.5 Summary
References
8 Quasi-Interval Bipartite Consensus
8.1 Problem Statement
8.2 A State Transition Matrix-Based Approach
8.3 Disagreement Behavior Analysis
8.4 Simulation Results
8.5 Summary
References
9 Leader-Contained Fluctuation
9.1 Problem Statement
9.2 A State Transition Matrix-Based Approach
9.3 Disagreement Behavior Analysis
9.3.1 Clustering Convergence of Union Leaders
9.3.2 Leader-Contained Fluctuation
9.4 Simulation Results
9.5 Summary
References
10 Local Characterization of Fluctuation Behaviors
10.1 Extended Structural Balance Theory
10.2 Local Disagreement Behavior Analysis
10.3 Simulation Results
10.4 Summary
References
Part III Dynamic Topologies
11 Behavior Analysis of Dynamic Signed Networks
11.1 Motivating Examples
11.2 Dynamic Signed Graphs
11.2.1 Basic Notions
11.2.2 Structural Balance and Connectivity
11.2.3 Dynamic Signed Graphs with WSPR Properties
11.3 Dynamic Distributed Control
11.4 Dynamic Bipartite Consensus
11.4.1 Undirected Dynamic Signed Networks
11.4.2 Extensions to Directed Dynamic Signed Networks
11.5 Simulation Results
11.6 Summary
References
12 Behavior Analysis of Mixed-Order Signed Networks
12.1 Problem Statement
12.2 Stability Results of Signed Networks
12.2.1 Sign-Consistent Nonidentical Topologies
12.2.2 Sign-Inconsistent Nonidentical Topologies
12.3 Simulation Results
12.4 Summary
References
13 Concluding Remarks
