Cooperative Control of Multi-Agent Systems: An Optimal and Robust Perspective

247 Pages·2020·12.948 MB·English

by  Jianan Wang, Chunyan Wang, Ming Xin

Cooperative Control
of Multi-Agent Systems
An Optimal and Robust Perspective

Cooperative Control
of Multi-Agent Systems
An Optimal and Robust Perspective
Jianan Wang
Beijing Institute of Technology
School of Aerospace Engineering
Beijing, China
Chunyan Wang
Beijing Institute of Technology
School of Aerospace Engineering
Beijing, China
Ming Xin
University of Missouri
Department of Mechanical and Aerospace Engineering
Lafferre Hall, Columbia, MO, United States
Zhengtao Ding
University of Manchester
Department of Electrical and Electronic Engineering
Manchester, United Kingdom
Jiayuan Shan
Beijing Institute of Technology
School of Aerospace Engineering
Beijing, China
Series Editor
Quan Min Zhu
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Contents
Abouttheauthors ix
Preface xi
Acknowledgments xiii
PartOne Aboutcooperative control 1
1 Introduction 3
1.1 Background 3
1.1.1 Motivations 3
1.1.2 Controlarchitecturesandstrategies 5
1.1.3 Relatedapplications 6
1.2 Overviewofrelatedworks 8
1.2.1 Consensuscontrol 8
1.2.2 Formationcontrol 11
1.2.3 Otherrelatedresearch 12
1.2.4 Futureresearchtopics 13
1.3 Objectivesofthisbook 14
1.4 Bookoutline 15
2 Preliminaries 17
2.1 Matrixtheory 17
2.2 Stabilitytheory 18
2.3 Basicalgebraicgraphtheory 21
2.3.1 Basicdefinitions 21
2.3.2 Graphmatrices 23
2.3.3 Properties 24
2.4 Usefullemmasoninequalities 27
PartTwo Optimalcooperative control 29
3 Optimalconsensuscontrolofmultipleintegratorsystems 31
3.1 Problemformulation 31
3.2 Optimalconsensuscontrolwithobstacleavoidance
forsingle-integratorcase 33
3.2.1 Optimalconsensusalgorithm:single-integratorcase 33
3.2.2 Numericalexamples 40
3.3 Optimalconsensuscontrolwithobstacleavoidancefor
double-integratorcase 44
3.3.1 Optimalconsensusalgorithm:double-integratorcase 44
vi Contents
3.3.2 Numericalexamples 53
3.4 Conclusionremarks 56
4 Optimalcooperativetrackingandflockingofmulti-agentsystems 59
4.1 Optimalrendezvousandcooperativetrackingcontrolwithobstacle
avoidance 59
4.1.1 Problemformulation 59
4.1.2 Optimalrendezvousalgorithmwithobstacleavoidance 59
4.1.3 Numericalexamples 66
4.1.4 Extensiontocooperativetrackingproblemwithobstacle
avoidance 70
4.2 Optimalflockingcontroldesignwithobstacleavoidance 80
4.2.1 Problemformulation 80
4.2.2 Optimalflockingcontrolalgorithmdesign 82
4.2.3 Numericalexamples 90
4.3 Conclusionremarks 96
5 OptimalformationcontrolofmultipleUAVs 97
5.1 Problemformulation 97
5.2 Integratedoptimalcontrolapproachtoformationcontrolproblem 100
5.3 Numericalexamples 110
5.3.1 Formationcontrolwithoutobstaclesonthetrajectoriesof
UAVs 111
5.3.2 Formationcontrolwithtwoobstaclesonthetrajectoriesof
UAVs 116
5.4 Conclusionremarks 120
6 Optimalcoveragecontrolofmulti-robotsystems 123
6.1 Problemformulation 123
6.1.1 Voronoitessellationandlocationaloptimization 123
6.1.2 Potentialfieldmethodforcollisionavoidance 125
6.2 Coveragecontrollerdesignwithknowndensityfunction 126
6.2.1 Coveragecontrollerdesign 126
6.2.2 Numericalexamples 127
6.3 Coveragecontrollerdesignwithdensityfunctionestimation 128
6.3.1 Estimationbasedcoveragecontrollerdesign 128
6.3.2 Numericalexamples 130
6.4 Conclusionremarks 130
PartThree Robust cooperativecontrol 133
7 Robustconsensuscontrolofmulti-agentsystemswithinputdelay 135
7.1 Problemformulation 135
7.2 ConsensusofLipschitznonlinearsystemswithinputdelay:model
reductionmethod 137
Contents vii
7.2.1 Stabilityanalysisforsinglenonlinearsystem 137
7.2.2 Consensusanalysis 138
7.2.3 Controllerdesign 147
7.3 ConsensusofLipschitznonlinearsystemswithinputdelay:
truncatedpredictorfeedbackmethod 149
7.3.1 Finite-dimensionalconsensuscontrollerdesign 149
7.3.2 Overviewoftruncatedpredictorfeedbackapproach 149
7.3.3 Consensusanalysis 150
7.4 Numericalexamples 161
7.4.1 Acircuitexample 161
7.4.2 Numericalexamples 164
7.5 Conclusionremarks 166
8 Robustconsensuscontrolofmulti-agentsystemswithdisturbance
rejection 169
8.1 Problemformulation 169
8.2 Disturbancerejectionforadirectedgraph 171
8.2.1 Consensuscontrollerdesignwithdisturbancerejection 171
8.2.2 Consensusanalysis 172
8.3 Fullydistributedconsensusdisturbancerejection 173
8.3.1 Localinformationbaseddisturbancerejectioncontroller 173
8.3.2 Consensusanalysis 175
8.4 Disturbancerejectioninleader-followerformat 176
8.4.1 Leader-followerdisturbancerejectioncontroller 176
8.4.2 Consensusanalysis 178
8.5 Numericalexamples 179
8.6 Conclusionremarks 181
9 Robustconsensuscontrolofnonlinearoddpowerintegratorsystems 183
9.1 Problemformulation 183
9.2 Distributedcontrollerfornonlinearoddpowerintegratorsystems 185
9.3 Numericalexamples 192
9.3.1 Perturbedcase 192
9.3.2 Perturbation-freecase 193
9.4 Conclusionremarks 196
10 Robustcooperativecontrolofnetworkednegative-imaginary
systems 197
10.1 Problemformulation 197
10.1.1 NIsystemdefinition 197
10.1.2 TypicalresultsforNIsystems 198
10.2 Robustconsensuscontrolformulti-NIsystems 200
10.2.1 HomogeneousNIsystems 200
10.2.2 Robustoutputfeedbackconsensusalgorithmfor
homogeneousmulti-agentsystems 201
viii Contents
10.2.3 Convergencesetstudy 205
10.2.4 Numericalexamples 208
10.3 Robustconsensuscontrolofheterogeneousmulti-NIsystems 211
10.3.1 HeterogeneousNIsystems 211
10.3.2 Robustoutputfeedbackconsensusalgorithmfor
heterogeneousmulti-agentsystems 213
10.3.3 Numericalexamples 221
10.4 Extensiontorobustcooperativecontrol 224
10.5 Conclusionremarks 226
Bibliography 227
Index 239
About the authors
JiananWangiscurrentlyanAssociatedProfessorintheSchoolofAerospaceEngi-
neering at Beijing Institute of Technology, China. He received his B.S. and M.S. in
Control Science and Engineering from the Beijing Jiaotong University and Beijing
Institute of Technology,Beijing, China, in 2004 and 2007, respectively.He received
his Ph.D. in Aerospace Engineering at Mississippi State University, Starkville, MS,
USAin2011.Hisresearchinterestsincludecooperativecontrolofmultipledynamic
systems,UAVformationcontrol,obstacle/collisionavoidance,trustworthynetworked
system,andestimationofsensornetworks.HeisaseniormemberofbothIEEEand
AIAA.
ChunyanWangisanAssociatedProfessorintheSchoolofAerospaceEngineering
at Beijing Institute of Technology, China. He received the B.Eng. degree in auto-
maticcontrolfromDezhouUniversity,Shandong,China,in2006,theM.S.degreein
control theory and control engineering from Soochow University, Jiangsu, China, in
2009,theM.Sc.degreeinelectricalandelectronicengineeringfromtheUniversityof
Greenwich,London,U.K.,in2012,andthePh.D.degreeincontrolsystemsfromthe
University of Manchester, Manchester, U.K., in 2016. He was a Research Associate
with the School of Electrical and Electronic Engineering, University of Manchester
from2016to2018.Hiscurrentresearchinterestsincludecooperativecontrol,robust
control,androbotics.
MingXinisaProfessorintheDepartmentofMechanicalandAerospaceEngineering
atUniversityofMissouri,US.HereceivedtheB.S.andM.S.degreesfromtheNan-
jing University of Aeronautics and Astronautics, Nanjing, China, in 1993 and 1996,
respectively,bothinautomaticcontrol,andthePh.D.degreeinaerospaceengineering
fromtheMissouriUniversityofScienceandTechnology,Rolla,MO,USA,in2002.
Hehasauthoredandcoauthoredmorethan120technicalpapersinhisresearchareas.
Hisresearchinterestsincludeoptimizationtheoryandapplications,estimation/filter-
ingandsignalprocessing,andcontrolofnetworkeddynamicsystems.Dr.Xinwasthe
recipientoftheU.S.NationalScienceFoundationCAREERAwardin2009.Heisan
AssociateFellowofAIAAandaSeniorMemberofAAS.
ZhengtaoDingisaProfessorintheDepartmentofElectricalandElectronicEngineer-
ing at University of Manchester, UK. He received the B.Eng. degree from Tsinghua
University,Beijing,China,andtheM.Sc.degreeinsystemsandcontrolandthePh.D.
degreeincontrolsystemsfromtheUniversityofManchesterInstituteofScienceand
Technology, Manchester, U.K. He was a Lecturer with Ngee Ann Polytechnic, Sin-
gapore, for ten years. In 2003, he joined the University of Manchester, Manchester,