Consensus Tracking of Multi-agent Systems with Switching Topologies

By Lijing Dong and Sing Kiong Nguang

Consensus Tracking of Multi-agent Systems with Switching Topologies takes an advanced look at the development of multi-agent systems with continuously switching topologies and relay tracking systems with switching of agents. Research problems addressed are well defined and numerical examples and simulation results are given to demonstrate the engineering potential. The book is aimed at advanced graduate students in control engineering, signal processing, nonlinear systems, switched systems and applied mathematics. It will also be a core reference for control engineers working on nonlinear control and switched control, as well as mathematicians and biomedical engineering researchers working on complex systems.

• Discusses key applications and the latest advances in distributed consensus tracking methods
• Offers a clear and comprehensive overview on the recent development of multi-agent systems with switching topologies
• Offers graduate students and beginning engineers a core reference on complex systems analysis and cooperative control

• Language: English
• Publisher: Academic Press
• Release date: Apr 8, 2020
• ISBN: 9780128189412

Lijing Dong

Lijing Dong received the B.E. and the Ph.D. degree from the School of Automation, Beijing Institute of Technology, Beijing, China, in 2010 and 2016, respectively. From 2013 to 2014, she was a visiting scholar with the Department of Electrical and Computer Engineering, University of Auckland. Currently, she is a Lecturer at School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University. Her current research interests include multi-agent systems and distributed control systems. She has obtained the authorization of multiple invention patents. In 2016, she got the first prizes of science and technology award from China Railway Society and innovation achievement award from China Industry-University-Research Institute Collaboration Association. She has published over 20 refereed journal and conference papers on multi-agent systems, large-scale complex systems and has/had served as reviewer of a number of international journals.

Book preview

Consensus Tracking of Multiagent Systems with Switching Topologies

Lijing Dong

School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, P.R. China

Sing Kiong Nguang

Department of Electrical, Computer, and Software Engineering, University of Auckland, Auckland, New Zealand

Table of Contents

Cover image

Title page

Copyright

About the authors

Acknowledgment

Chapter 1. Introduction

Abstract

Chapter Outline

1.1 A brief of multiagent systems

1.2 Multiagent systems with time-varying topologies

1.3 Multiagent systems with node failures/actuator faults

1.4 Applications of multiagent systems

References

Further reading

Chapter 2. Multiagent systems with continuously switching topologies

Abstract

Chapter Outline

2.1 Introduction

2.2 First-order multiagent systems with continuously switching topologies

2.3 Second-order multiagent systems with continuously switching topologies

2.4 Conclusion

References

Chapter 3. High-order multiagent systems with continuously switching topologies

Abstract

Chapter Outline

3.1 Introduction

3.2 Problem description

3.3 High-order multiagent systems with continuously switching topologies

3.4 High-order multiagent systems with continuously switching topologies based on polytopic model

3.5 Conclusion

References

Chapter 4. High-order multiagent systems with time delays and continuously switching topologies based on polytopic model

Abstract

Chapter Outline

4.1 Introduction

4.2 Problem description

4.3 Main section

4.4 Numerical examples

4.5 Conclusion

References

Chapter 5. Sliding mode control for multiagent systems with continuously switching topologies based on polytopic model

Abstract

Chapter Outline

5.1 Introduction

5.2 Preliminaries and problem description

5.3 Sliding mode controller design and stability analysis

5.4 Sliding mode control for multiagent systems with disturbances

5.5 Conclusion

References

Chapter 6. Cooperative relay tracking strategy for multiagent systems with assistance of Voronoi diagrams

Abstract

Chapter Outline

6.1 Introduction

6.2 Voronoi diagrams

6.3 Relay tracking algorithm

6.4 Controller design and stability analysis

6.5 Numerical examples

6.6 Conclusion

References

Further reading

Chapter 7. Stability of a class of multiagent relay tracking systems with unstable subsystems

Abstract

Chapter Outline

7.1 Introduction

7.2 Related preliminaries

7.3 Problem formulation

7.4 Controller design and stability analysis

7.5 Disturbance attenuation analysis

7.6 Numerical examples

7.7 Conclusion

References

Chapter 8. Multiagent relay tracking systems with damaged agents and time-varying number of agents

Abstract

Chapter Outline

8.1 Introduction

8.2 Relay tracking systems with damaged agents

8.3 Relay tracking systems with time-varying number of agents

8.4 Conclusion

References

Chapter 9. Multiagent relay tracking systems with time-varying number of agents and time delays

Abstract

Chapter Outline

9.1 Introduction

9.2 Linear relay tracking systems with time-varying number of agents and time delays

9.3 Nonlinear relay tracking systems with time-varying number of agents and time delays

9.4 Conclusion and discussions

References

Chapter 10. Finite time stability analysis and coordination strategies of multiagent relay tracking systems

Abstract

Chapter Outline

10.1 Introduction

10.2 Stability analysis of nonlinear multiagent relay tracking systems over a finite time interval

10.3 Finite-time coordination control of multiagent systems for target tracking with node failures and active replacements

10.4 Conclusion

References

Further reading

Chapter 11. Conclusions and future research

Abstract

Chapter Outline

11.1 Conclusions

11.2 Future research

References

Appendix A

A.1 Notations

A.2 Assumptions and lemmas

Index

Copyright

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About the authors

Lijing Dong

Lijing Dong received the BE and the PhD degree from the School of Automation, Beijing Institute of Technology, Beijing, China, in 2010 and 2016, respectively. From 2013 to 2014, she was a visiting scholar with the Department of Electrical and Computer Engineering, University of Auckland. Currently, she is an Associate Professor at School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University. Her current research interests include multiagent systems and distributed control systems. She has obtained the authorization of multiple invention patents. In 2016 she got the first prizes of science and technology award from China Railway Society and innovation achievement award from China Industry-University-Research Institute Collaboration Association. She has published more than 20 refereed journal and conference papers on multiagent systems and large-scale complex systems and has/had served as reviewer of a number of international journals.

Sing Kiong Nguang

Sing Kiong Nguang received the BE (with first class honors) and the PhD degree from the Department of Electrical and Computer Engineering of the University of Newcastle, Callaghan, Australia, in 1992 and 1995, respectively. Currently, he is a Chair Professor at the Department of Electrical, Computer, and Software Engineering, University of Auckland, Auckland, New Zealand. He has published more than 300 refereed journal and conference papers on nonlinear control design, nonlinear control systems, nonlinear time-delay systems, nonlinear sampled-data systems, biomedical systems modeling, fuzzy modeling and control, biological systems modeling and control, and food and bioproduct processing. He has/had served on the editorial board of a number of international journals. He is the chief editor of the International Journal of Sensors, Wireless Communications and Control.

Acknowledgment

We gratefully acknowledge the support from the National Natural Science Foundation of China under Grant 61903022.

Chapter 1

Introduction

Abstract

Multiagent systems (MASs) have become a hot research area in the recent two decades due to the wide applications to mobile robots, unmanned aerial vehicles, autonomous underwater vehicles, and satellites. Consensus tracking problem is a typical issue of MASs. In practical the velocity of each maneuvering agent is time varying and the communication radius of each agent is finite. Therefore the communication topology between the agents may change from time to time, and tracking problem of MASs under time-varying topologies is of vital necessity.

Keywords

Consensus tracking; AUV; multiagent systems; node failures; time-varying topologies; UAV

Chapter Outline

Outline

1.1 A brief of multiagent systems 2

1.1.1 Related graph theory 4

1.1.2 Consensus control 5

1.1.3 Formation control 6

1.1.4 Consensus tracking 8

1.2 Multiagent systems with time-varying topologies 10

1.2.1 Multiagent systems with switching topologies 10

1.2.2 Multiagent systems with jointly connected topologies 11

1.2.3 Multiagent systems with continuously time-varying topologies 13

1.3 Multiagent systems with node failures/actuator faults 14

1.4 Applications of multiagent systems 17

1.4.1 Application to cooperative robots 17

1.4.2 Application to multi-unmanned aerial vehicle 18

1.4.3 Application to intelligent train control 19

References 20

Further reading 27

Multiagent systems (MASs) have become a hot research area in the recent two decades due to the wide applications to mobile robots, unmanned aerial vehicles (UAVs), autonomous underwater vehicles, and satellites. Consensus tracking problem is a typical issue of MASs. In practical the velocity of each maneuvering agent is time varying and the communication radius of each agent is finite. Therefore the communication topology between the agents may change from time to time, and tracking problem of MASs under time-varying topologies is of vital necessity.

This chapter summarizes the recent development of MASs with different types of time-varying topologies, such as switching topologies, jointly connnected topologies, and continuously time-varying topologies. Then, systems with node failures or actuator faults are introduced and the concept of relay tracking is presented. Finally, the applications of multiagent systems are introduced.

1.1 A brief of multiagent systems

Inspired by the group activities of humans and collective behavior of insects or birds, researchers have done a lot of work to explain this kind of phenomena [1,2]. Over the last two decades, MASs have received much attention from researchers in various areas [3–12]. Numerous results have been achieved under various circumstances such as consensus tracking with switching topologies [13,14], the disturbance-rejection consensus [15], finite-time tracking control [16,17], pinning adaptive–impulsive control [18], and optimal coordination [19,20].

A MAS is formed by multiple autonomous agents that are capable of sensing the environment, moving, and information processing. An agent can be an UAV, or an unmanned ground vehicle (UGV), or a spacecraft, or an autonomous train, or a robot, etc. A MAS is of high efficiency, low cost, and reliability which make it an effective solution to solve complex tasks. The complex task is divided into multiple small tasks, each of which is assigned to a specific agent, namely, the complex task is accomplished through cooperation of individual agents, which is the salient feature of MASs.

Currently, there are many different categories in the cooperative control of MASs. Consensus control, formation control, and tracking control are three of the most attractive ones.

Since consensus of MASs is a fundamental problem in this research area, it has attracted increasing attention of researchers from various disciplines of engineering, biology, and science. In networks of agents, consensus means to reach an agreement regarding a certain quantity of interest that depends on the state of all agents. A consensus algorithm is an interaction rule that specifies the information exchange between an agent and all of its neighbors on the network. The consensus problems have been formulated as consensus of leaderless problems or leader-following problems [21–23]. For a cooperative MAS, leaderless consensus means that each agent updates its state based on local information of its neighbors such that all agents eventually reach an agreement on a common value, while leader-following consensus means that there exists a virtual leader that specifies an objective for all agents to follow.

Formation control is another hot topic, where a group of interconnected agents is controlled to cooperatively move with a desired formation pattern. The desired formation could be time invariant [24,25] or time varying [26,27]. Specifically, Lu et al. [25] obtain sufficient conditions guaranteeing the exponentially converging speeds for both time-invariant and time-varying formation problems of MASs with directed graph interconnection topologies and time-varying coupling delays. Wang et al. [27] design a novel event-triggered integral sliding mode control strategy that makes sure the high-order agents achieve a time-varying formation.

Tracking control is a typical issue of MASs [7,9,11,13,28]. Many researchers have achieved significant results [13,29–32] on the tracking problem as it is an important topic in MASs’ research area. Consensus tracking of a target can be regarded as leader-following consensus problem. For example, Hajshirmohamadi et al. [33] propose unified event-triggered framework that requires the agents to transmit their information when the triggering condition is satisfied. In Ref. [34], two adaptive event-triggered communication schemes are presented for the consensus tracking control of MASs with stochastic actuator failures. Linear and dynamic-gain-based nonlinear observers are designed for solving the consensus tracking problem of second-order MASs with disturbance in Ref. [35].

Since agents are in various specific forms, consequently, the dynamics of agents are in different mathematical models, which can be generally categorized into linear and nonlinear dynamics. In the past few years, the MASs with integer dynamics [36,37] have been widely studied by many researchers due to its simple construction and convenience to analyze. Certainly, there are some researchers spend efforts on MAS with nonlinear dynamics [21,38] or switching topologies [22,39].

Single-integrator dynamics described by (1.1) and double-integrator dynamics described by (1.2) are basic forms of agents [35,40,41].

(1.1)

are the state and the control input of the ith agent.

(1.2)

is the velocity state of the ith agent.

As a direct extension of the study of the MASs with single-integrator or double-integrator dynamics, systems with general linear dynamics described by (1.3) are also studied recently [33].

(1.3)

is state vector of iis the control input.

As a further extension, MASs with nonlinear dynamics have attracted much attention of researchers. Nonlinear systems include first-, second-, and high-order dynamics, in which the second-order dynamics described by (1.4) is the most common form in the literature [42,43].

(1.4)

is the nonlinear dynamics of ith agent.

1.1.1 Related graph theory

with nonnegative elements. The nodes within the communication range of node i are called the set of neighbors of node imeans node j is beyond the communication range of node iwe say that node has self-loop. In this book, it is assumed that no self-loop exists.

Specifically, as illustrated in Fig. 1.1, the dash circles represent communication ranges of agents. Agent i and agent j On the other hand, agent k is not within agent iIn terms of consensus tracking problem, the target is involved. bi decides whether agent i means agent i Denote ℬ=diag{b1, b2, …, bN}.

Figure 1.1 Illustration of communication range and topology.

The in-degree and out-degree of node i are, respectively, defined as

.

of graph G where

1.1.2 Consensus control

Consensus control is a typical and fundamental problem in the multiagent coordination system. The consensus problem depicts how several autonomous agents reach agreements under the effect of distributed control algorithms based on local information. As depicted in Fig. 1.2, reaching agreement means the states of all agents are the same.

Figure 1.2 Illustration of consensus.

The definition of consensus is given as follows:

Definition 1.1

for each agent i, such that

(1.5)

Specifically, there are some different types of consensus, such as

(1.6)

The corresponding types of consensus in (1.6) are referred to as average-consensus, max-consensus, and min-consensus, respectively. Thus a general name is defined as χ-consensus.

In a MAS, agents only have local information received from its neighbors. Therefore the typical distributed linear control algorithm is designed as (1.7).

(1.7)

is the control parameter to be designed.

It should be noted that (1.7) is a typical form for consensus control for first-order system. The first- and second-order consensus problem for MASs has been intensively investigated [44–53].

In Ref. [54], necessary and sufficient conditions are achieved for mean square consentability of the averaging protocol for discrete-time agents communicating through a stochastic directed network. Kim et al. [7] address the problem of consensus of MIMO LTI MASs under a time-varying network by designing compensators with coupled output of each agent. The authors in Refs. [13,55] propose a new kind of network topology-dependent multiple Lyapunov functions for analyzing the synchronization behavior of MASs with switching topologies. In Ref. [56], leader-following consensus problem for multiple Euler–Lagrange systems with connectivity preservation is extensively investigated. Specifically, the authors in Refs. [57,58] investigate consensus problems of high-order MASs with switching topologies.

1.1.3 Formation control

Formation control is a consensus-related problem. Conceptually, a formation of multiple agents can be obtained using consensus theoretical framework [59,60]. However, for a consensus problem, the states of all agents are expected to finally reach a common value. In terms of formation control, each agent moves according to the prescribed trajectory, while all the agents achieve some desired formation pattern [61] as shown in Fig. 1.3.

Figure 1.3