Table Of ContentConsensus Tracking of Multiagent
Systems with Switching Topologies
Consensus Tracking
of Multiagent Systems
with Switching
Topologies
Lijing Dong
Schoolof Mechanical,Electronic and Control Engineering,
Beijing Jiaotong University, Beijing, P.R. China
Sing Kiong Nguang
Department ofElectrical,Computer,and Software Engineering,
University of Auckland, Auckland, New Zealand
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Contents
Abouttheauthors ix
Acknowledgment xi
1. Introduction 1
1.1 Abriefofmultiagentsystems 2
1.1.1 Relatedgraphtheory 4
1.1.2 Consensuscontrol 5
1.1.3 Formationcontrol 6
1.1.4 Consensustracking 8
1.2 Multiagentsystemswithtime-varyingtopologies 10
1.2.1 Multiagentsystemswithswitchingtopologies 10
1.2.2 Multiagentsystemswithjointlyconnectedtopologies 11
1.2.3 Multiagentsystemswithcontinuouslytime-varying
topologies 13
1.3 Multiagentsystemswithnodefailures/actuatorfaults 14
1.4 Applicationsofmultiagentsystems 17
1.4.1 Applicationtocooperativerobots 17
1.4.2 Applicationtomulti-unmannedaerialvehicle 18
1.4.3 Applicationtointelligenttraincontrol 19
References 20
Furtherreading 27
2. Multiagent systems with continuously switching
topologies 29
2.1 Introduction 29
2.2 First-ordermultiagentsystemswithcontinuouslyswitching
topologies 30
2.2.1 Mainresults 30
2.2.2 Anumericalexample 34
2.3 Second-ordermultiagentsystemswithcontinuouslyswitching
topologies 36
2.3.1 Consensustrackingwithdouble-integratordynamics 37
2.3.2 Consensustrackingwithsecond-ordernonlineardynamics 40
2.3.3 Numericalexamples 42
2.4 Conclusion 45
References 46
v
vi Contents
3. High-order multiagent systems with continuously
switching topologies 47
3.1 Introduction 47
3.2 Problemdescription 48
3.3 High-ordermultiagentsystemswithcontinuouslyswitching
topologies 49
3.3.1 Stabilityanalysis 50
3.3.2 Simulationresults 53
3.4 High-ordermultiagentsystemswithcontinuouslyswitching
topologiesbasedonpolytopicmodel 54
3.4.1 Stabilityanalysis 56
3.4.2 Anumericalexample 58
3.5 Conclusion 63
References 64
4. High-order multiagent systems with time delays and
continuously switching topologies based on polytopic
model 65
4.1 Introduction 65
4.2 Problemdescription 66
4.3 Mainsection 67
4.4 Numericalexamples 73
4.5 Conclusion 85
References 85
5. Sliding mode control for multiagent systems with
continuously switching topologies based on polytopic
model 87
5.1 Introduction 88
5.2 Preliminariesandproblemdescription 89
5.3 Slidingmodecontrollerdesignandstabilityanalysis 89
5.3.1 Slidingmodecontrollerdesign 89
5.3.2 Stabilityanalysis 91
5.3.3 Numericalexamples 94
5.4 Slidingmodecontrolformultiagentsystemswithdisturbances 98
5.4.1 Slidingmodecontrollerdesignforsystemswith
disturbances 98
5.4.2 Stabilityanalysisforsystemswithdisturbances 99
5.4.3 Numericalexamples 102
5.5 Conclusion 102
References 105
Contents vii
6. Cooperative relay tracking strategy for multiagent
systems with assistance of Voronoi diagrams 107
6.1 Introduction 107
6.2 Voronoidiagrams 109
6.3 Relaytrackingalgorithm 113
6.4 Controllerdesignandstabilityanalysis 115
6.5 Numericalexamples 120
6.6 Conclusion 127
References 128
Furtherreading 129
7. Stability of a class of multiagent relay tracking systems
with unstable subsystems 131
7.1 Introduction 131
7.2 Relatedpreliminaries 132
7.3 Problemformulation 134
7.4 Controllerdesignandstabilityanalysis 136
7.5 Disturbanceattenuationanalysis 139
7.6 Numericalexamples 141
7.7 Conclusion 149
References 149
8. Multiagent relay tracking systems with damaged
agents and time-varying number of agents 151
8.1 Introduction 151
8.2 Relaytrackingsystemswithdamagedagents 152
8.2.1 Problemformulation 153
8.2.2 Relaytrackingalgorithm 154
8.2.3 Controllerdesignandstabilityanalysis 155
8.2.4 Anumericalsimulation 161
8.3 Relaytrackingsystemswithtime-varyingnumberofagents 163
8.3.1 Preliminariesandproblemformulation 164
8.3.2 Mainresultsofrelaytrackingsystemswithtime-varying
numberofagents 168
8.3.3 Anumericalsimulation 171
8.4 Conclusion 172
References 174
9. Multiagent relay tracking systems with time-varying
number of agents and time delays 177
9.1 Introduction 177
9.2 Linearrelaytrackingsystemswithtime-varyingnumberof
agentsandtimedelays 178
viii Contents
9.2.1 Problemformulation 178
9.2.2 Mainresults 181
9.2.3 Numericalsimulations 189
9.3 Nonlinearrelaytrackingsystemswithtime-varying
numberofagentsandtimedelays 192
9.3.1 Relatedpreliminaries 192
9.3.2 Stabilityanalysis 195
9.3.3 Numericalsimulations 200
9.4 Conclusionanddiscussions 204
References 206
10. Finite time stability analysis and coordination
strategies of multiagent relay tracking systems 207
10.1 Introduction 208
10.1.1 Finitetimeboundedness 208
10.1.2 Finitetimecoordinationrelaystrategies 209
10.2 Stabilityanalysisofnonlinearmultiagentrelaytracking
systemsoverafinitetimeinterval 209
10.2.1 Relaytrackingproblemformulation 209
10.2.2 Stabilityanalysisoverafinitetimeinterval 212
10.2.3 Stabilityanalysisforsystemssubjecttodisturbances 214
10.2.4 Numericalexamples 215
10.3 Finite-timecoordinationcontrolofmultiagentsystemsfor
targettrackingwithnodefailuresandactivereplacements 218
10.3.1 Trackingproblemdescriptionandfundamentals 220
10.3.2 Event-triggeredcoordinationstrategy 222
10.3.3 Nonsingularterminalslidingmodecontrollerdesign 224
10.3.4 Finitetimeanalysiswithmodifiedslidingmodecontrol 226
10.3.5 Stabilityanalysisofsystemswithagentreplacements 228
10.3.6 Numericalsimulations 229
10.4 Conclusion 235
References 235
Furtherreading 237
11. Conclusions and future research 239
11.1 Conclusions 239
11.1.1 Consensustrackingcontrolofsystemswith
continuouslyswitchingtopologies 239
11.1.2 Relaytrackingcontrolofsystemswithagent
replacements 240
11.2 Futureresearch 240
11.2.1 Generalnonlinearmultiagentsystems 241
11.2.2 Cooperativecontrolalgorithmsbasedondeeplearning 241
References 241
AppendixA 243
Index 249
About the authors
LijingDong
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 inter-
nationaljournals.
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, respec-
tively. 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 confer-
ence 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 con-
trol, 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
InternationalJournalofSensors,Wireless Communications and Control.
ix
Acknowledgment
We gratefully acknowledge the support from the National Natural Science
Foundation of China under Grant 61903022.
xi
