Event-Triggered Cooperative Control: Analysis and Synthesis

195 Pages·2022·3.549 MB·English

by  Wenying Xu, Daniel W. C. Ho, Jinde Cao

Wenying Xu
Daniel W. C. Ho
Jinde Cao
Event-Triggered
Cooperative
Control: Analysis
and Synthesis
Event-Triggered Cooperative Control: Analysis
and Synthesis
· ·
Wenying Xu Daniel W. C. Ho Jinde Cao
Event-Triggered Cooperative
Control: Analysis
and Synthesis
WenyingXu DanielW.C.Ho
SchoolofMathematics DepartmentofMathematics
SoutheastUniversity CityUniversityofHongKong
Nanjing,Jiangsu,China HongKong,China
JindeCao
SchoolofMathematics
SoutheastUniversity
Nanjing,Jiangsu,China
ISBN 978-981-19-5653-9 ISBN 978-981-19-5654-6 (eBook)
https://doi.org/10.1007/978-981-19-5654-6
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Preface
Fordecades,multi-agentsystems(MASs)havebeenattractedconsiderableresearch
interest due to their wide applications in practice such as sensor networks, power
grid systems, brain and cyber-physical systems. In general, an MAS is composed
ofmultipleintelligentagentsinteractingthroughwiredorwirelesscommunication
links. MASs are able to accomplish tasks that are difficult or impossible for an
individualagenttoaccomplish.Assuch,howtodevelopdistributedalgorithmsfor
agents to carry out prescribed tasks in a cooperative fashion becomes one of the
focusesonstudyingMASs.
Itisworthwhiletonotethatmostofliteratureconcerningcooperativecontrolof
MAS implicitly assumed that agents collaborate with their neighbors in a perfect
networkenvironment.Suchanassumptionis,however,notalwaystrueinpractice
owingtounavoidablecommunication/networkconstraints.Forexample,communi-
cationresourcescouldbelimitedandcostlyinmanyreal-worldscenarios,andthus
itisnecessarytomitigateunnecessarywasteofcommunicationenergyasmuchas
possible.Inaddition,thenetworksecurityissuehasbecomeanemergingresearch
focusinsignalprocessingandcontrolengineeringcommunities.InMASs,multiple
agents are connected via shared (sometimes even public) network media, which
leads to that information transmission is easily disrupted or maliciously manipu-
lated by attackers. Therefore, in this book, we investigate the cooperative control
ofMASswithunavoidablecommunicationconstraintsincomplexnetworkcircum-
stances.Specialattentionwillbefocusedoncommunicationconstraintscausedbya
limitedcommunicationbandwidthandvariousmeansofcyber-attacks.Thesekinds
ofconstraintscouldinvalidatethecontrolprotocolandaffectthecooperativecontrol
performance.
The book provides a systematic and in-depth introduction to distributed event-
triggered cooperative control for MASs from a theoretical perspective. The major
research topics include: a unified design and analysis framework for centralized,
clustered and distributed event-triggered schemes (ETSs); fully distributed design
for event/self-triggered schemes; resilient event-triggered control under malicious
attacks;andvariousmethodstoavoidZenobehavior.Thecomprehensiveandsystem-
atictreatmentofevent-triggeredcommunication(ETC)andcontrolinMASsisoneof
v
vi Preface
themajorfeaturesofthebook,whichisparticularlysuitedforreaderswhoareinter-
ested in learning principles and methods to deal with communication constraints
in MASs and to design energy-saving control protocols. The book can benefit
researchers, engineers, and graduate students in the fields of complex networks,
smart grids, applied mathematics, electrical and electronic engineering, computer
engineering,etc.
Thebookisorganizedasfollows:
•
Chapter1beginswiththebackgroundofMASs.Subsequently,theorganizationof
thisbook,someimportantdefinitions,usefullemmas,andsomebasicknowledge
aboutgraphtheoryareintroduced.
•
Chapter2discussestheleader-followingconsensusissueofMASswithgeneral
lineardynamicsbyusingETSs.Threetypesofschemes,namely,centralizedETS,
distributed ETS, and clustered ETS are constructed to achieve leader-following
consensus.AunifiedanalyticalframeworkisdevelopedfortheproposedETSand
theexclusionofZenobehavior.
•
Chapter 3 forms an impulsive framework to analyze the effect of the clustered
ETSs on leader-following consensus of MASs, where three different cases are
considered,thatis,availableagents’states,availabledisturbedagents’states,and
availableagents’outputs.Then,thecorrespondingevent-triggeredprotocolsare
constructed for achieving (L∞) leader-following consensus, and Zeno behavior
canbeexcludedinthesecases.
•
Chapter4studiesthedynamicsofMASswithamultilayerstructure,proposinga
novellayeredevent-triggeredscheme(LETS)forconsensus.ThisLETSempha-
sizesonsynchronousinformationtransmissioninthesamelayerbutasynchronous
messageupdatebetweendifferentlayers,whichdiffersfromtheexistingcentral-
ized or distributed ETSs. Moreover, under the LETS, agents in different layers
achieveasymptoticconsensuseventuallyandZenobehaviorissuccessfullyelimi-
nated.Furthermore,analgorithmisprovidedtoavoidcontinuouseventdetection,
verifiedbyanumericalexample.
•
Chapter5proposesadistributededgeevent-triggeredscheme(EETS)ofMASs
viaacommunicationbuffertoreduceunnecessaryupdateofcontrollersinduced
by fast information transmission. The characteristics and advantages of the
distributed EETS are stated in this chapter. Then, another case is investi-
gated where edge information transmission is subject to quantization, and a
distributedquantizededgeevent-triggeredcontrolprotocolisproposed.Notethat
such a quantized protocol guarantees asymptotic consensus instead of bounded
consensus in most of the existing literature. Meanwhile, both distributed and
quantizedEETSshavenontrivialpropertiesofexcludingZenobehavior.Further-
more, an algorithm is provided to avoid continuous event detection, and hence
thecommunicationtrafficofthewholenetworkisreducedsignificantly.
•
Chapter6isintendedtosolvethefullydistributedandobserver-basedconsensus
control problem of MASs with general linear dynamics under ETC. Two
novelevent-triggeredstrategiesnamedadaptivedynamicevent-triggered(ADET)
schemesforone-to-allandone-to-oneETCarewelldeveloped,inwhichon-line
Preface vii
triggeringparametersassociatedwitheachnodeoredgeanddynamicthresholds
with updating laws are introduced, respectively. The one-to-one ETC provides
a flexible self-regulated transmission mode. An effective fully distributed and
observer-basedconsensusprotocolisdevelopedappropriatelywithavailablelocal
measurement outputs, under which the agents are not required to have a priori
knowledge of any global information. Further discussion on the efficiency of
ADETstrategiesandcomparisonbetweenstate-basedandobserver-basedADET
controlareprovidedtoenrichthedistributedresources-awarecontrolframework.
•
Chapter7proposesafullydistributedself-triggeredschemeforachievingsecond-
order consensus in MASs. In this framework, an iterative evaluation method is
constructed to guarantee that any global information, especially the eigenvalue
information of Laplacian matrix, is not involved in the self-triggered scheme.
The proposed self-triggered scheme is able to efficiently schedule information
transmissionforeachcommunicationchannel,basedonwhichboththecommu-
nicationfrequencyofeachchannelandthecostofeventdetectionaresignificantly
reduced. In addition, some sufficient conditions for achieving the second-order
consensusandaverageconsensusareobtained,andZenobehaviorissuccessfully
eliminated.
•
Chapter 8 develops a fully distributed framework to investigate the coopera-
tive behavior of MASs in the presence of distributed Denial-of-Service attacks
launched by multiple adversaries. In such an insecure network environment,
two kinds of communication schemes, i.e., sample-data and ETC schemes, are
discussed. Then, a fully distributed control protocol with strong robustness and
highscalabilityiswelldesigned.Thisprotocolguaranteesasymptoticconsensus
againstdistributedDoSattacks.Fortheevent-triggeredcase,twoeffectivedynam-
icalETSsareproposed,whichareindependentofanyglobalinformation.Such
ETSsdonotexhibitZenobehaviorevenintheinsecureenvironment.
•
Chapter 9 investigates the second-order consensus issue for MASs subject to
bothlimitedcommunicationresourcesandreplayattacks.First,anasynchronous
dynamic EETS for communication is developed to reduce the utilization of
networkresourcesintheabsenceofattacks.Then,wefurtherconsiderthecaseof
replayattackslaunchedbymultipleadversaries,underwhichthetransmittedinfor-
mationismaliciouslyreplacedbyapreviousunnecessarymessage.Toovercome
theimpactcausedbyreplayattacks,amodifieddynamicEETSandaneffective
attack-resilientconsensusprotocolarewellconstructed.Asaresult,theysuccess-
fullyguaranteesecond-orderconsensusinthepresenceofreplayattacks.Inaddi-
tion,internaldynamicvariablesareutilizedintheproposeddynamicEETSssuch
thatthetriggeringtimesequencedoesnotexhibitZenobehavior.
Nanjing,China WenyingXu
HongKong,China DanielW.C.Ho
Nanjing,China JindeCao
May2022
Acknowledgements
This work was supported in part by the National Natural Science Foundation of
ChinaunderGrant62173087,61922030,61803082,theNaturalScienceFoundation
ofJiangsuProvinceunderGrantBK20180367,theNationalKeyR&DProgramof
ChinaunderGrantNumbers2020YFA0714301,theKeyProjectofNationalNatural
Science Foundation of China under Grant Number 61833005, the Fundamental
ResearchfortheCentralUniversities,inpartbyResearchGrantsCounciloftheHong
Kong Special Administrative Region, China (CityU 11202819, CityU 11203521),
and CityU Strategic Research Grant 7005511, and in part by the Alexander von
HumboldtFoundationofGermany.
ix
Contents
1 Introduction .................................................. 1
1.1 Background ............................................. 1
1.2 ResearchProblems ....................................... 3
1.3 MathematicalPreliminaries ................................ 7
1.3.1 Consensus, Second-Order Consensus
andLeader-FollowingConsensus .................... 7
1.3.2 MathematicalModels .............................. 7
1.3.3 BasicTheoryonGraphsandMatrices ................ 8
1.4 SomeUsefulLemmas ..................................... 9
References .................................................... 10
2 Event-TriggeredLeader-FollowingConsensusAnalysis ........... 15
2.1 ProblemStatement ....................................... 16
2.2 CentralizedETS ......................................... 16
2.3 DistributedETS .......................................... 21
2.4 ClusteredETS ........................................... 26
2.5 DiscussiononEventDetection ............................. 29
2.6 Summary ............................................... 31
References .................................................... 32
3 AnImpulsiveFrameworkforEvent-TriggeredConsensus
Analysis:TheClusteredCase ................................... 35
3.1 Event-TriggeredState-FeedbackProtocol .................... 36
3.1.1 ProblemStatement ................................. 36
3.1.2 ConsensusAnalysisBasedonImpulsiveControl
Framework ....................................... 38
3.1.3 TheCasewithExternalDisturbance .................. 41
3.2 Event-TriggeredOutput-FeedbackProtocol .................. 45
3.2.1 ProblemStatement ................................. 45
3.2.2 Consensus Analysis via Impulsive Control
Framework ....................................... 47
xi
xii Contents
3.3 NumericalExamples ...................................... 50
3.4 Summary ............................................... 58
References .................................................... 58
4 A Layered Event-Triggered Scheme for Multi-layered
DirectedNetworkTopology .................................... 61
4.1 ModelFormulation ....................................... 62
4.2 DesignandAnalysisofLETS .............................. 63
4.3 ReducingFrequencyofEventDetection ..................... 69
4.4 NumericalExample ...................................... 71
4.5 Summary ............................................... 73
References .................................................... 75
5 Distributed Edge Event-Triggered Consensus Protocol
withCommunicationBuffer ................................... 77
5.1 ProblemStatement ....................................... 78
5.2 DistributedEETConsensusScheme ........................ 78
5.3 QEETConsensusScheme ................................. 82
5.4 DiscussiononEventDetection ............................. 85
5.5 NumericalExamples ...................................... 86
5.6 Summary ............................................... 89
References .................................................... 89
6 Fully Distributed Event-Triggered Control: Adaptive
DynamicEvent-TriggeredSchemes ............................. 91
6.1 ProblemStatement ....................................... 92
6.2 One-to-AllETCScheme .................................. 93
6.2.1 TheADETStrategyforOne-to-AllETC .............. 93
6.2.2 ConsensusCriteriaUnderOne-to-AllETC ............ 95
6.3 One-to-OneETCScheme ................................. 97
6.3.1 TheADETStrategyforOne-to-OneETC ............. 97
6.3.2 ConsensusCriteriaUnderOne-to-OneETC ........... 98
6.4 NumericalExamples ...................................... 106
6.4.1 One-to-AllETCUndertheObserver-BasedADET
Strategy .......................................... 107
6.4.2 One-to-OneETCUndertheObserver-BasedADET
Strategy .......................................... 107
6.4.3 SomeComparisons ................................ 110
6.5 Conclusions ............................................. 112
References .................................................... 114
7 FullyDistributedSelf-TriggeredControlforSecond-Order
Consensus ................................................... 117
7.1 ProblemStatement ....................................... 118
7.2 DesignofSelf-triggeredScheme ........................... 119
7.3 AnalysisofSelf-triggeredScheme .......................... 123
7.4 NumericalExample ...................................... 135