Table Of ContentStudies in Systems, Decision and Control 248
Zhenwei Liu
Donya Nojavanzadeh
Ali Saberi
Cooperative
Control
of Multi-agent
Systems
A Scale-Free Protocol Design
Studies in Systems, Decision and Control
Volume 248
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· ·
Zhenwei Liu Donya Nojavanzadeh Ali Saberi
Cooperative Control
of Multi-agent Systems
A Scale-Free Protocol Design
ZhenweiLiu DonyaNojavanzadeh
CollegeofInformationScience SchoolofElectricalEngineering
andEngineering andComputerScience
NortheasternUniversity WashingtonStateUniversity
Shenyang,China Pullman,WA,USA
AliSaberi
SchoolofElectricalEngineering
andComputerScience
WashingtonStateUniversity
Pullman,WA,USA
ISSN 2198-4182 ISSN 2198-4190 (electronic)
StudiesinSystems,DecisionandControl
ISBN 978-3-031-12953-7 ISBN 978-3-031-12954-4 (eBook)
https://doi.org/10.1007/978-3-031-12954-4
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Thisbookisdedicatedto:
Myfamily:Yuan,Xinning,Yuan’sandmy
parents
(ZhenweiLiu)
Myfamily
(DonyaNojavanzadeh)
Mychildren:Ingmar,Ula,Dmitri,and
Mirabella
(AliSaberi)
and
thegloryofman.
Acknowledgements
Wewouldliketoexpressoursinceregratitudetoourcollaborators,AntonA.Stoor-
vogel,SaeedLotfifard,MeirongZhang,andDmitriSaberi,fortheircontributionsin
publishingthepapersthatformthepartialresultsinthisbook.
The writing of this monograph was supported in part by the National Natural
ScienceFoundationofChinaunderGrant62273084.
Shenyang,China ZhenweiLiu
Pullman,USA DonyaNojavanzadeh
Pullman,USA AliSaberi
October2022
vii
Contents
1 Introduction .................................................. 1
1.1 CooperativeControlofMulti-agentSystems ................. 1
1.2 Outline ................................................. 4
2 NotationsandPreliminaries .................................... 7
2.1 LinearAlgebra ........................................... 7
2.2 SignalandSystemNorms ................................. 9
2.3 Graphs .................................................. 10
2.4 Multi-agentSystemsandGraphs ........................... 11
2.5 Passivity ................................................ 14
2.5.1 Continuous-TimeSystem .......................... 14
2.5.2 Discrete-TimeSystem ............................. 18
3 SynchronizationofContinuous-TimeMAS ...................... 21
3.1 ProblemFormulation ..................................... 21
3.2 ScalableOutputSynchronization ........................... 24
3.2.1 ArchitectureoftheProtocol ........................ 24
3.2.2 ProtocolDesign .................................. 25
3.2.3 SpecialCase:HomogeneousMAS .................. 29
3.3 ScalableRegulatedOutputSynchronization .................. 31
3.3.1 ArchitectureoftheProtocol ........................ 31
3.3.2 ProtocolDesign .................................. 32
3.4 NumericalExamples ...................................... 35
4 SynchronizationofDiscrete-TimeMAS ......................... 39
4.1 HomogeneousMASwithNon-introspectiveAgents ........... 39
4.1.1 ProblemFormulation .............................. 39
4.1.2 ScalableStateSynchronization ..................... 41
4.2 HeterogeneousMASwithIntrospectiveAgents ............... 46
4.2.1 ScalableOutputSynchronization .................... 49
4.2.2 ScalableRegulatedOutputSynchronization .......... 53
4.3 NumericalExamples ...................................... 57
ix
x Contents
5 Regulated State Synchronization of Homogeneous MAS
inthePresenceofInputDelays ................................. 61
5.1 ProblemFormulation ..................................... 61
5.2 ScalableRegulatedStateSynchronization .................... 65
5.2.1 SolvabilityConditions ............................. 65
5.2.2 ProtocolDesign .................................. 66
5.2.3 SpecialCase:MASwithFull-StateCoupling ......... 73
5.3 NumericalExamples ...................................... 77
5.3.1 Example1:Continuous-TimeMAS ................. 77
5.3.2 Example2:Discrete-TimeMAS .................... 79
6 StateSynchronizationofHomogeneousContinuous-Time
MASinthePresenceofNonuniformCommunicationDelays ...... 83
6.1 ProblemFormulation ..................................... 83
6.2 ScalableStateSynchronization ............................. 86
6.2.1 Solvability Condition and Protocol Design
for Arbitrary Constant Reference Trajectory
y ∈ Rp ......................................... 86
r
6.2.2 NecessaryandSufficientSolvabilityConditions
andProtocolDesign ............................... 92
6.3 NumericalExamples ...................................... 95
7 StateSynchronizationofHomogeneousDiscrete-TimeMAS
inthePresenceofNonuniformCommunicationDelays ........... 99
7.1 ProblemFormulation ..................................... 99
7.2 ScalableStateSynchronization ............................. 102
7.3 NumericalExamples ...................................... 107
8 RegulatedOutputSynchronizationofHeterogeneousMAS
inthePresenceofNonuniformCommunicationDelays ........... 113
8.1 ProblemFormulation ..................................... 113
8.2 ScalableRegulatedOutputSynchronization .................. 117
8.2.1 ArchitectureoftheProtocol ........................ 117
8.2.2 ProtocolDesign .................................. 118
8.3 NumericalExamples ...................................... 127
8.3.1 Continuous-TimeMAS ............................ 127
8.3.2 Discrete-TimeMAS ............................... 130
9 DelayedRegulatedSynchronizationofContinuous-TimeMAS
inthePresenceofUnknown,Non-uniform,andArbitrarily
LargeCommunicationDelays .................................. 135
9.1 HomogeneousMASwithNon-introspectiveAgents ........... 135
9.1.1 ProblemFormulation .............................. 135
9.1.2 ScalableDelayedRegulatedStateSynchronization .... 139
9.2 HeterogeneousMASwithIntrospectiveAgents ............... 146
9.2.1 ProblemFormulation .............................. 146
Contents xi
9.2.2 Scalable Delayed Regulated Output
Synchronization .................................. 147
9.3 NumericalExamples ...................................... 151
9.3.1 Example1.HomogeneousMAS .................... 152
9.3.2 Example2.HeterogeneousMAS .................... 155
10 DelayedRegulatedSynchronizationofDiscrete-TimeMAS
inthePresenceofUnknown,Non-uniform,andArbitrarily
LargeCommunicationDelays .................................. 159
10.1 HomogeneousMASwithNon-introspectiveAgents ........... 159
10.1.1 ProblemFormulation .............................. 159
10.1.2 ScalableDelayedRegulatedStateSynchronization .... 162
10.2 HeterogeneousMASwithIntrospectiveAgents ............... 169
10.2.1 ProblemFormulation .............................. 169
10.2.2 Scalable Delayed Regulated Output
Synchronization .................................. 171
10.3 NumericalExamples ...................................... 175
10.3.1 Example1.HomogeneousMAS .................... 176
10.3.2 Example2.HeterogeneousMAS .................... 177
11 GlobalRegulatedStateSynchronizationofHomogeneous
Continuous-Time MAS with Non-introspective Agents
inthePresenceofInputSaturation ............................. 185
11.1 ProblemFormulation ..................................... 185
11.2 Scalable Global Regulated State Synchronization
viaNonlinearDynamicProtocols ........................... 189
11.2.1 ProtocolDesignforPartial-StateCouplingCase ....... 189
11.2.2 ProtocolDesignforFull-StateCouplingCase ......... 192
11.3 Scalable Global Regulated State Synchronization
viaLinearDynamicProtocols .............................. 194
11.3.1 ProtocolDesignforPartial-StateCouplingCase ....... 194
11.3.2 ProtocolDesignforFull-StateCouplingCase ......... 197
11.4 NumericalExamples ...................................... 199
11.4.1 Example1:NonlinearProtocolDesign ............... 199
11.4.2 Example 2: Linear Observer-Based Protocol
Design .......................................... 201
12 GlobalRegulatedStateSynchronizationofHomogeneous
Discrete-Time MAS with Non-introspective Agents
inthePresenceofInputSaturation ............................. 205
12.1 ProblemFormulation ..................................... 205
12.2 Scalable Global Regulated State Synchronization
viaNonlinearDynamicProtocols ........................... 209
12.2.1 ProtocolDesignforFull-StateCouplingCase ......... 211
12.2.2 ProtocolDesignforPartial-StateCouplingCase ....... 216
