# Cooperative Control of Complex Network Systems with Dynamic Topologies

## Guanghui Wen, Wenwu Yu, Yuezu Lv, Peijun Wang

- 304 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android

# Cooperative Control of Complex Network Systems with Dynamic Topologies

## Guanghui Wen, Wenwu Yu, Yuezu Lv, Peijun Wang

## About This Book

Far from being separate entities, many social and engineering systems can be considered as complex network systems (CNSs) associated with closely linked interactions with neighbouring entities such as the Internet and power grids. Roughly speaking, a CNS refers to a networking system consisting of lots of interactional individuals, exhibiting fascinating collective behaviour that cannot always be anticipated from the inherent properties of the individuals themselves.

As one of the most fundamental examples of cooperative behaviour, consensus within CNSs (or the synchronization of complex networks) has gained considerable attention from various fields of research, including systems science, control theory and electrical engineering. This book mainly studies consensus of CNSs with dynamics topologies - unlike most existing books that have focused on consensus control and analysis for CNSs under a fixed topology. As most practical networks have limited communication ability, switching graphs can be used to characterize real-world communication topologies, leading to a wider range of practical applications.

This book provides some novel multiple Lyapunov functions (MLFs), good candidates for analysing the consensus of CNSs with directed switching topologies, while each chapter provides detailed theoretical analyses according to the stability theory of switched systems. Moreover, numerical simulations are provided to validate the theoretical results. Both professional researchers and laypeople will benefit from this book.

## Frequently asked questions

## Information

# CHAPTER 1

## Introduction

## 1.1 Complex network systems

## 1.2 Definitions of synchronization and consensus

*N*agents. Without loss of generality, we label the

*N*agents as agents $$, respectively. The dynamics of agent

*i*, $$, are represented by

*i*. A particular case is the general linear time-invariant MASs with the dynamics of agent

*i*are described by

**Definition 1.1**

*Consensus of the MAS (1.1) is said to be achieved if for arbitrary initial conditions*$$, $$,

*i*whose dynamics are described by (1.1) the follower

*i*, $$, and call the agent whose dynamics are described by (1.4) the leader.

**Definition 1.2**

*Consensus tracking (or leader following consensus)*

*of the MAS with the followers given by*(1.1)

*and the leader given by*(1.4)

*is said to be achieved if for some given initial conditions*$$ and $$, $$,

**Remark 1.1**

*The mathematical definitions for synchronization of complex networks and consensus of MASs are precisely similar. However, some differences between these two topics are briefly summarized as follows from our viewpoint.*

*A complex network typically contains a great number of individual nodes (e.g., the Internet) while the scale of an MAS may be relatively quite small (e.g., a team of several robots).**The objective of synchronization control is to make the states of a large-scale network achieve state agreement under some given inner linking matrices by selecting only the coupling strength, while the objective of consensus is to make the states of agents achieve state agreement by designing the gain matrices as well as the coupling strength.**Significant attention has been paid to revealing the relationship between the statistical properties (e.g., the degree distribution, the average path length, and the symmetry) of network topology and the synchronizability of complex networks within the context of synchronization in complex networks, while in the context of consensus of MASs, much attention has been focused on addressing the relationship between the algebraic properties (e.g., the algebraic connectivity for undirected interaction topology and the general algebraic connectivity for directed interaction topology) of interaction topology and the consensusability.*

*Practical applications of consensus of CNSs:*Achieving consensus in CNSs is critical for controlling these CNSs and thus helpful in dealing with various distributed control problems for practical network systems. For instance, reaching consensus of velocities for all individual agents is a precondition in achieving flocking in various second-order CNSs [117]. In another instance, frequency synchronization of multiple generator units within a power system is one of the most important issues in power system stability control [221]. In addition, clock synchronization among sensors within wireless sensor networks is highly desirab...