Network-Induced Constraints in Networked

Network-InducedConstraintsinNetworked

ControlSystems—ASurvey

LixianZhang,Member,IEEE,HuijunGao,SeniorMember,IEEE,andOkyayKaynak,Fellow,IEEE

Abstract—Networkedcontrolsystems(NCSs)have,inrecentyears,broughtmanyinnovativeimpactstocontrolsystems.How-ever,greatchallengesarealsometduetothenetwork-inducedimperfections.Suchnetwork-inducedimperfectionsarehandledasvariousconstraints,whichshouldappropriatelybeconsid-eredintheanalysisanddesignofNCSs.Inthispaper,themainmethodologiessuggestedintheliteraturetocopewithtypicalnetwork-inducedconstraints,namelytimedelays,packetlossesanddisorder,time-varyingtransmissionintervals,competitionofmultiplenodesaccessingnetworks,anddataquantizationaresur-veyed;theconstraintssuggestedintheliteratureonthefirsttwotypesofconstraintsareupdatedindifferentcategorizingways;andthoseonthelatterthreetypesofconstraintsareextended.IndexTerms—Analysisanddesignofnetworkedcontrolsystems,network-inducedconstraints,networkedcontrolsystems.

I.INTRODUCTION

whichthecomponents,i.e.,controllers,sensorsandactu-atorsarespatiallydistributedandconnectedviaacertaindigitalcommunicationnetworkThenetworkscanbeeitherthecon-trolnetworksthathavebeenaroundforaconsiderableamountoftimeforspecializedreal-timepurposessuchascontrolareanetwork(CAN),BACnet,Fieldbus,or,morerecently,thewire-lineorwirelessEthernet,evenInternet,forgeneral-purposedatacommunicationtasks.AscommentedinalmostalltheliteratureonNCSs,themotivationstoconstructsuchacontrolsystemvianetworksarethelowinstallationandmaintenancecosts,highreliability,increasedsystemflexibility,anddecreasedwiring.Suchbenefitshavegivenagreatimpetustoextensiveapplica-tionsofNCSsinmanyfields,suchasthefewthatarebrieflydiscussedhereafter.

Vehicleindustry:Inatypicalmodernautomobile,forin-stance,thetechnologyofCAN-baseddatacommunicationamongalmostalltheelectromechanicalmoduleseliminatestheproblemofextensivewiringinalimitedspace.Theinteractionsofthesubsystems,e.g.,enginecontrol,transmissioncontrol,

ManuscriptreceivedJuly30,2011;revisedDecember09,2011;acceptedJune22,2012.DateofpublicationSeptember18,2012;dateofcurrentver-sionDecember19,2012.TheworkwassupportedinpartbyNationalNat-uralScienceFoundationofChina(60904001),OutstandingYouthScienceFundofChina(60825303)and973Project(2009CB320600)inChina.Paperno.TII-11-357.

L.ZhangandH.GaoarewiththeSpaceControlandInertialTechnologyResearchCenter,HarbinInstituteofTechnology,Harbin150080,China(e-mail:lixianzhango@hit.edu.cn;hjgao@hit.edu.cn).

O.KaynakiswiththeDepartmentofElectricalandElectronicEn-gineering,BogaziciUniversity,Bebek,Istanbul80815,Turkey(e-mail:okyay.kaynak@boun.edu.tr).

Colorversionsofoneormoreofthefiguresinthispaperareavailableonlineathttp://ieeexplore.ieee.org.

DigitalObjectIdentifier10.1109/TII.2012.22190

Fig.1.TheCAN-basednetworkedcontrolsystemsinatypicalautomobile(from[2],reproducedwithpermission).

N

ETWORKEDcontrolsystems(NCSs)arecontrolsystemsin

anti-lockedbrakingsystem(ABS),andaccelerationslipregu-lation(ASR)system,arenetworked[1].AnillustrationontheuseofCANinanautomobileisgiveninFig.1[2].

Network-BasedProcessControlEngineering:Nowadays,theFieldbus,industrialEthernet,etc.,havebeenwidelyandsuccessfullyappliedinmanyprocesscontrolengineeringsys-tems,suchasthewastewatertreatmentprocess,asillustratedinFig.2[3].Inthisapplication,informationonvariousprocessvariables,e.g.,waterlevel,pHfactor,temperature,chemicaloxygendemand(COD),arecollectedbythecontroldevices(PLCs)locatedatseparatedstations,andthentransmittedviaindustrialEthernettocentralcontrolroomsforprocessingandintegratedanalysis.

Teleoperation:Generally,teleoperationistheexecutionofataskbyapairofmaster–slavemanipulatorsinwhichthelattermaybelocatedalongdistanceawayonEarthoreveninspace[4].AnillustrativeschemeofInternet-basedteleopera-tioncanbeseeninFig.3.

OtherapplicationsofNCSscanbefoundinpowersystems[5],transportationsystems[6],andcontrolsystems[7],etc.Inrecentyears,toeasethepracticalapplicationofNCSs,con-siderableeffortshavebeenspentandsomeprogresshasbeenmadeintopicssuchasthefollowing:1)modelingofNCSs;

2)stabilityandperformanceanalysis;3)networkedcontrolandestimation;

4)network-basedfaultdetectionandtolerance;5)identificationvianetworks;

AmongthevastliteratureonNCSsthatisavailabletodate,wereferthereadersespeciallytothebooks[8]–[10],surveypapers[11]–[14],specialissues[15]–[19],Ph.D.dissertations[20]–[22],andthenumerousreferencesthereintoenablethemtoseethestateoftheartinNCSs.

1551-3203/$31.00©2012IEEE

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Fig.2.Networkedcontrolsystemsinatypicalwastewatertreatmentplant(from[3],reproducedwithpermission).

Fig.3.AtypicalschemeofInternet-basedteleoperation.

InanNCS,thenetworkmayexistinthechannelsensor-to-controllerand/orthechannelcontroller-to-actuator,whicharealsotermedasthefeedbackchanneland/ortheforwardchannel,respectively.ThesystemcomponentsinNCSsarecommonlycallednetworknodes,e.g.,“asensornode”(itmaycorrespondtoasinglesensororacollectionofsensors).Theexistenceofthenetworkissuchthatthedataflowinapacket-basedmannerbetweenthenetworknodes.AgeneralarchitectureofNCSsisillustratedinFig.4.

Comparedwiththetraditionallypoint-to-pointanalogfeed-backcontrolsystems,insertinganetworktoacontrolloopmaycauseaseriesofproblemsthatwilldeterioratethesystemper-formanceorevendestabilizethesystem.Differentlevelsofnet-work-inducedimperfectionsincludethefollowing:1)timedelays;

2)packetlossesanddisorder;

3)time-varyingpackettransmission/samplingintervals;4)competitionofmultiplenodesaccessingnetwork;5)dataquantization;

6)clockasynchronizationamonglocalandremotenodes;7)networksecurityandsafety.

Duringthepastdecades,extensivestudiesonnetwork-in-ducedimperfectionshavebeencarriedoutbyboththecontrol

Fig.4.GeneralarchitectureofNCSs.

andthecommunicationcommunitiesassumingdifferentsce-narios,andvariousmethodologieshavebeenproposedonhowtocopewiththeimperfections.Whileessentiallyeliminatingthenetwork-inducedimperfectionscannotbeseparatedfromtheimprovementsofthecommunicationinfrastructureitself,de-velopingappropriatecontroltheoriesandapproachesinNCSstoovercometheseimperfectionsisofgreatnecessityandsig-nificance.Manysystematicresultsinthisregardhaveunfoldedwithrespecttothesourcesandthemodelingoftheseimperfec-tionsandthedifferentapproachesforhandlingthem.

ReviewsontheadvancesmadeinNCSsnevercease.Somesummarieshavebeengivenindifferentphases,suchasthesurveysbyTipsuwanandChowin2003[12]ontime-delayproblemsinNCSs,andYangin2006[13],Hespanhaetal.in2007[14]onadditionaltypesofimperfectionsinNCSs,suchaspacketlosses,time-varyingsamplingintervals,andcompeti-tionofmultiplepackettransmissionsand,morerecentlyGuptaandChowin2010[11]onotherissuesofNCSs,suchasnet-worksecurityandotherrealisticconsiderations.

Inthissurvey,weshallfocusonnetworkimperfectionsandreviewtherelatedstudies,payingspecialattentiontothosecar-riedoutsincethepublishingdatesofthesurveysreferredto.Itisworthnoticingthat,foraparticularNCS,thedifferenttypesofimperfectionslistedabovemaynotoccursimultaneouslyinpractice,andtheeffectsofsomeimperfectionsincertainnet-worksmaybeminor,e.g.,thetimedelaycanbeignoredinareal-timenetwork,andthequantizationerrorsarenegligibleinhighbandwidthEthernet.Weattempttopresentalltheimpor-tantresultsonalltheaspectsherebutnotemphasizetheirap-plicabilityortheirlimitationsifanysincetheencounteredsce-nariovaries.Whilecoveringallthecontributionsisimpossible,wedevoteourselvestoidentifyingexplicitresearchlinesandhelpingcategorizethemethodologies.Thesurveyisorganizedasfollows.First,SectionIIgivestheoverviewofeachtypeofnetwork-inducedimperfection.Regardingtheimperfectionsasnetwork-inducedconstraints,SectionIIIpresentsthemainsurveyofthemethodologiesintheanalysisanddesignofNCSs.

ZHANGetal.:NETWORK-INDUCEDCONSTRAINTSINNETWORKEDCONTROLSYSTEMS—ASURVEY405

SectionIVprovidestheconclusionandliststheexpectedfuturelinesofresearch.

II.CONSTRAINTSCAUSEDBYNETWORK-INDUCED

IMPERFECTIONSTONCSS

Thenetwork-inducedimperfectionslistedabovecanbeviewedasconstraintsintheanalysisanddesignofNCSs.Inthissection,weshallanalyzethesourceofsuchnetwork-in-ducedconstraints,presenttheirimpacts,andintroducethemainmethodologiessuggestedinliteratureforhandlingthem.

Timedelays:ThedelaysinaNCSarecomposedofthecom-putationaldelaysineachcomponentofthesystemduetothecertainprocessingspeedofthedigitaldevices,thenetworkac-cessdelay,i.e.,thetimeaqueuednetworkpackethastowaitbe-forebeingsentout,andthetransmissiondelaythroughthenet-workmedium.Generally,inNCSs,thecomputationaldelayisnegligiblecomparedwiththeothertwoclassesofdelaysthatarecommonlycalledthenetwork-induceddelays.Asshowninthestudiesontraditionaltime-delaysystems,thedelaywillcausepoorperformanceoreveninstabilityoftheclosed-loopsystem.DifferentwaysofmodelingthedelaysinNCSleadtodifferentresultsofanalysisandsynthesiswithdifferentconservatism,whichmayyetbeneededindifferentscenariosinpractice.Packetlossesanddisorder:Duetonetworktrafficcongestionandpacketstransmissionfailures,packetlossesareinevitableinnetworksespeciallyinawirelessnetwork[23].Anexces-sivelylongpropagationdelayofapacketcanbealsoviewedasapacketlost.Severeconsecutivepacketlossesamounttothedisconnectionofanetwork.Therefore,dealingwithpacketlossesinNCSsisanewchallengethatisneverencounteredinpoint-to-pointcontrolsystems.Howtodeterminetheaccept-ablelowerboundonthepackettransmissionrateisamajorconcerninthearea.Itistobenotedthatthestudiescarriedoutonthisconstraintaresignificantnotonlyforthosenonac-knowledgementprotocolslikeuserdatagramprotocol(UDP),butalsoforthereliabletransmissionprotocolsliketransmissioncontrolprotocol(TCP).Thepacketdisorderphenomena,whichmeansthattheindicesofthepacketstransmittedovernetworksaremixed,canhappenifthenetwork-induceddelaysaremorethanonesampling/transmissioninterval.Whileastraightwayofsolvingtheprobleminmostofstudiesistodiscardtheoldpacketsifthelatestpackethasalreadyarrivedatthereceiver,wewillbereviewingtherelativelyfewerreferencesaddressingtheproblem,aswellasprovidingourextraviewpointstotheproblem.

Time-varyingtransmission/samplingintervals:AsNCSsbelongtothespectrumofdigitalcontrol,theanalogsignalsofplantoutputsneedbesampledatsensornodesbeforetheyareencodedintodigitalsignalsandpackagedintothepacketstransmittedovernetworks.Usually,constantsamplinginNCSscannotbeensured,andthetime-varyingsamplingphenomenaoccurnotonlyduetothefactorstypicalinallpoint-to-pointdigitalcontrolsystems(e.g.,clockaccuracy),butalsototheschedulingofthepackettransmissionsinthecontextofmul-tiplesensornodes.Likewise,iftherearemultiplepacketstobetransmittedatcontrollernodes,thetransmissionintervalswillbeverylikelytobetimevarying.Infact,thetimebetweentwosuccessivetransmission/samplingcanbeveryuncertainandsignificantlylarge;consequently,thesystemstabilityand/orperformancewillbecompromised.Itisstraightforwardthatthefastertheinformationcommunicates,thebettertheperformancethatthesystemcanachieve;amajorresearchlinewithrespecttothistypeofnetwork-inducedconstraintisthereforetofindtheso-calledmaximumallowabletransferinterval(MATI).Althoughtherearesomeworksaddressingthecontrolproblemsofmanycomplexdynamicsystemsundertime-varyingsampling,theproblembecomesmoretypicalanddifficultinNCSswhenothertypesofnetwork-inducedconstraintscoexist.

Competitionofmultiplenodesaccessingnetwork:Com-petitionofmultiplenodesaccessingthenetworkisatypicalnetwork-inducedphenomenonoccurringinthecontextofmultiplepacketstransmission.ActuallymostNCSscomprisemultiplenetworknodes,andeachofthenodesmaycorrespondtoacollectionofsensors,actuators,orcontrollers.Besides,inmanyapplicationswherethesensorsandtheactuatorsaredistributedoveralargephysicalarea,itisalsoimpossibletoputallthemeasurementsorcontrolinputdataintoonenetworkpacket.Althoughsomeresearcherssupposethescenarioofonepackettransmissionandfocusontheafore-introducednet-work-inducedconstraintstofacilitatetheanalysisanddesignintheory,themultiplepacketstransmissionarefarmorepracticalasnowadaysthescaleofNCSsrapidlygrows.Itisthereforevaluabletosolvetheproblemofthecontentionofnodes,whichisalsodefinedasaschedulingprobleminNCSsliterature.Withinthetopic,theanalysisanddesignofappropriatepro-tocolsdeterminingwhichnodesaccessanetworkwhenandhowisamajorconcern.Inparticular,asintroducedintheconstraintoftime-varyingtransmissionintervals,thecompeti-tionofnodesdirectlygivesrisetotime-varyingtransmissionsofthemeasuredoutput.Wewillthuspayspecialattentiontothosereferencesaddressingthetightrelationsbetweenthetwoconstraints.

Dataquantization:Dataquantizationisacommonphenom-enoninalldigitalcontrolsystems,andthushasbeenaclassicaltopicinconventionaldigitalcontroltheoryevenbeforethepop-ularityofNCSs.Quantizationmeansthatproceduressuchasthetransformationfromanalogsignalstodigitalsignals,thecom-puter-basedrealizationofadesignedcontroller(e.g.,thequan-tizationofsomecoefficientsrelatedtocontrollergains),andthetruncationofwordscausedbycalculationsincertaincontrolal-gorithms.Ithasbeenwellrecognizedindigitalcontrolsystemsthatthequantizationmainlyresultsfromthefinitewordlength,andthequantizationerrorwillaffecttheclosed-loopsystemsta-bilityand/orperformance.InanNCS,thequantizationnaturallyexistsduetotheessenceofdigitalcontrol.Weregarditasatyp-icalnetwork-inducedconstraintinthissurveysinceitisinsepa-rablefromthelimitednetworkbandwidth.QuiteafewopinionsinNCSliteratureinsistonthatthequantizationeffectcanbeig-noredsinceenoughnumberofbitsineachtransmittedpacketcanbeguaranteedbythecurrentnetworktechnologies.How-ever,theincreasinglyexpandedinvestigationsonthequantiza-tionprobleminNCSsarestillusefulinthescenariowherethequantizationimpactisverynegative.

Inadditiontotheabovefivecategoriesoftypicalconstraints,theconstraintsofclockasynchronizationandnetworksecurityshouldalsobeconsideredinthepracticalconstructionandop-erationofanNCS.However,thesetwoconstraintsdonotgen-erallyfallintothescopeofcontrol-orientedinvestigationsonNCSs.Thus,thestateofartonthemwillnotbepursuedin

406IEEETRANSACTIONSONINDUSTRIALINFORMATICS,VOL.9,NO.1,FEBRUARY2013

thissurvey.Efficientsolutionsfortheclocksynchronizationandnetworksecurityproblemscanbefoundin[26]and[27],respectively.

III.MAINSURVEYONMETHODOLOGIES

FOR

NETWORK-INDUCEDCONSTRAINTS

Inthissection,themethodologiesusedforthehandlingofthefirstfiveconstraintsintroducedinSectionIIwillbesurveyed.Indiscussionsforeachconstraint,weshallfirstreviewtherefer-encesfocusingonit,thenthosereferencesthatsimultaneouslyaddressitandsomeoftheotherconstraints.A.TimeDelays

Generallyspeaking,thenetwork-induceddelaysarecausedbymainlytworeasons—thetransmissiondistanceandthenet-worktrafficcongestion.Thetransmissiondistanceisanobviousfactor.Longerdistancesgiverisetoalongertransmissiontimeunderthesameconditions(networkbandwidth,protocols,etc.).Therefore,ifonebroadenstheconceptofNCSstoincludetheparadigmssuchasInternet-basedremotecontrolandteleoper-ation,thesituationofdelaysmorethanonesamplingintervalwillbemorefrequentlyencountered.Thus,remotecontroloverInternetofthoseplantshavingastrictreal-timerequirementisinappropriate.Ontheotherhand,thedelayalsocomesfromthenetworktrafficcongestionduetothelimitedbandwidthofthecommunicationchannels.Itmeansevenforashorttransmis-siondistance,thedelaymaybeveryuncertain,andprobablymorethanonesamplinginterval,especiallywhenthenetworkissharedwithothercontrolloopsorotherdataexchangetasks.Therefore,atthestageofdesigningNCSsarchitectures,con-trolstrategies,andnetworkprotocols,thenetwork-inducedde-laysshouldbeconcretelycharacterizedaccordingtotheprac-ticalscenarios.

ThecharactersofthedelaysinNCSs,oncethespecificnet-worksareselected,canbesummarizedandcategorizedintothreepairs:

1)constantversustime-varyingdelay;2)deterministicversusstochasticdelays;

3)delaysmallerthanonesamplingintervalandotherwise.Suchclassificationscanbejustifiedindiverseapplicationsusingdifferentnetworks.Forinstance,untilrecently,theassumptionofconstantdelaywassupposedtoholdinCANprotocolorincircumstanceswhenbuffersareusedatnet-worknodes(thenonequivalentdelaysareincreasedtobethesame).Nowadays,moreandmorenetworkprotocols(suchasEthernet)cannotensureaconstantdelay.Thus,thestudiescopingwithtime-varyingdelaysaremoreprevalent,evenifthesamplingintervalinthecontrolledplantsorprocessesislargerthanthedelayintroducedbythenetwork.Forthetime-varyingdelays,twodivisionscanbefoundintheliterature,i.e.,thenondeterministicallyvaryingorstochasticallyvarying.Intheformer,thevariationofdelaysisnotknownaprioributtheinstantaneousvalueisavailabletodesignersinrealtime.Thelatterimpliesthatthevariationofthedelaysisassociatedwithsomestatisticaldescriptions,eitherthecaseofthecurrentdelaybeingindependentofthepreviousones,orthecaseofsomecorrelationbetweenthecurrentdelayandthepreviousones.Asforthethirdclassification,oneneedstonotethatalthoughnetworktechniquesareincreasinglyupdated,itisstillverylikelyforsomeNCSstopossessdelaysmorethanonesampling

interval,say,thoseNCSsconstructedviathenetworkseasilysubjecttohighnetworkloads.Formoredetailsonthesourcesofnetwork-induceddelaysandtheclassificationsofthemindifferentcharacters,wereferthereadersto[21],[28]–[30],andthereferencestherein.

Differentdelays,togetherwithspecificplants,callfordif-ferentcontrolstrategiesinNCSs.TipsuwanandChow[12]summarizethetypicalmethodologiesusedinliteratureupto2003inmodeling,analysis,andsynthesisofNCSsinvolvedwithdelays,includingtheLQGapproach,thehybridsystemapproach,andtheperturbationapproach,etc.ThesurveyofHespanhaetal.[14]complementsthiswork,byfocusingontheadvancesmadefrom2003to2007,suchastheapproachofmodelingNCSsbydelayeddifferentialequations(DDEs),theswitchedsystemsapproach,etc.In[13],additionalap-proachesforthedelayissuearereviewed,includingthetwoMarkovchainsmodelingapproachbyZhangetal.[25]forbothfeedbackandforwardchannels,etc.Althoughthesesurveyscoveralmostallofthemethodologiesfornetwork-induceddelayssuggestedbeforetheirpublicationsdates,itshouldberealizedthat,inthecurrentliterature,agrowingnumberoftheirreferencesarebeingcontinuouslyupdated.

Inthispaper,byconsideringtheadvancesreportedsince2007,weclassifythemethodologiesfordealingwithtime-varyingdelaysintotwoframeworks,withtheobjectivebeingtoenablethefutureresearcherstoclassifytheirwork.Weshalldefinethefirstframeworkasrobustnessframework,whichmeansthatthecontroldesignisrobustovertime-varyingdelays.AtypicalapproachintheframeworkistoregardanNCSasatraditionalinput-delaysystem,e.g.,inlinearcases,asfollows:

whereisthestate-feedbackcontrollergain,and

arethetime-varyingdelayinthefeedbackchannelandforward

channel,respectively,with

.istheinitialcondition.

Themodelcaneitherconsidertheforwardchannelorthefeedbackchannelonly,orlumpsthedelaysinbothchannelsintoone(themanipulationcanbefrequentlyseenintheliterature

that

).SubsequentstepsintheapproacharetoconstructanappropriateLyapunov–Krasovskiifunctionalandderivetheconditionsofsystemstability,performance,con-trollerdesign,orfilterdesign,dependingontheproblemstobehandled.Thebasiclinesoftheapproacharethesameasthoseusedforconventionaltime-delaysystems.Typicalworksinthisregardinclude[31]and[32].Noticethatinthesetreatments,theso-calledtime-stampinformationexistinginthepacketsisnotused.Thiscanbeseenfromsomeworkswithrespecttocontrollerdesignthatthecontrollergainisindependentofthetime-delayvalues.Forotherapproachesintheframework,wequotethefuzzy-model-basedapproachwherethefuzzyrulesarebasedonthesizeofnetwork-induceddelays.Therefore,ifthedesigntakesallpossibledelaysinagivenfinitesetintoac-count,thenthedesignedcontrollerswillberobustoverthevari-ationsofthedelaysdespitewhatsizetherealdelayis.Atypicalworkinthisrespectcanbeseenin[33],whereitisassumedthat

ZHANGetal.:NETWORK-INDUCEDCONSTRAINTSINNETWORKEDCONTROLSYSTEMS—ASURVEY407

TABLEI

TYPICALREFERENCESWITHRESPECTTONETWORK-INDUCEDDELAYS

hasdifferentvalues,andthe

numberoffuzzyrulesisalso.Therefore,theNCSisregardedastheblendingofthelocalmodelswiththefollowingrules.

Rule

:IFis,THENtheNCSmodelis

whereandarethediscretizedsystemmatrices.TheglobalmodeloftheNCScanbeobtainedasfollows:

whereisthemembershipfunction,andisthefuzzystate-feedbackcontrollergain.Asimilarwayofmodelingthedelaysbyfuzzysetscanbealsofoundin[34],wherethefuzzyrulesarebasedonthesystemoutputerrorbutinherentlycorrelatedwiththedelays.Insummary,wecharacterizethosemethodologiesthatdonotusethedelaysizeinformationintherobustnessframework.Therunningmodeiscommonlytimedrivenatsensornodes,andeithertimedrivenoreventdrivenatcontroller(oractuator)nodes.Whiletheanalysisanddesignintheframeworkissimpler,itisrelativelyconservativeignoringthespecialtiesofNCSs.Infact,wecanidentifythreeattributesofNCSscomparedwiththeconventionaldelaysystemsasstatedbelow.Theycanleadtoanotherframeworkofadaptationtodelays,whichwewilladdressafterwards.

1)ThefirstspecialtyofNCSsisthatdataovernetworksaretransmittedinpackets,which,takingEthernetforexample,arecapableofpackaginglargeamountofdatasuchasasequenceofcontrolcommands.

2)AnotherdifferencebetweenNCSsandconventionaldelaysystemsisthetime-stamptechniqueintheformer.Becauseofthis,thereceiversitecanexactlyknowhowlongthetransmissionofthecurrentnetworkpackethasexpired.3)Theactuatorsiteisprovidedwithreasonableselectionin-telligenceifthenetworkaccessfunctioncanberealized,i.e.,theactuatorcanbeassumedtobesmart.

Thepointsabovewillenabletherealizationsoftheap-proachesbelongingtothesecondframework,whichweshalldefineastheadaptationframework.Inwhatfollows,twoapproachesintheframeworkwillbediscussed.

ThefirstoneistomodelanNCSasastochasticornondeter-ministicswitchedsystem,withthecontrollergaindependingonthesizeofdelays.Inthisapproach,thesmartactuatorreceivesasetofcontrollergainsandselectsoneaccordingtothecurrentdelaysize.Theearlyworksthatusethestochasticswitchedsys-temsapproachinclude[35]byXiaoetal.,whereanaugmentedclosed-loopsystemisestablishedbyconsideringalldelaysinaboundedset,andtheresultingsystemisaMarkovjumplinearsystem.Zhangetal.[25]extendtheideaandusetwoMarkov

chainstomodelthedelaysinbothfeedbackandforwardchan-nels.There,thediscretizedcontrolledplantisconsideredas

Thecontrolinputcanbeobtainedas

ThedelaysandaresubjecttoMarkovchainwith

where,andand.

Notethatin[25],thedesignedcontrollergaindependsonthecurrentfeedbackchanneldelayandthepreviousforwardchanneldelay.Yet,thefirstspecialityofNCSslistedaboveen-ablesasetofcontrolcommandstobesentfromthecontrollersite,bywhichthecontrolcommandcanbeselectedatthesmartactuatoraccordingtothecurrentforwardchanneldelay.Inad-ditiontothestochasticdescriptionofdelayvariations,nondeter-ministicdescriptionscanbeconsideredwithintheframework,i.e.,assumingthetransitionsprobabilitiesarecompletelyun-knownandthevariationsofthetimedelaysarestatedependentortimedependent.Thelatterscenariocanbehandledbyusingthewell-knowndwelltimeoraveragedwelltimeswitchingtechniques.In[40]and[41],theauthorsassumethatthenet-workaccessdelaysarethemaindelayinthesystem.Thereg-ulationproblem,stabilityanalysis,anddisturbanceattenuationarestudied.

Asthesecondtypicalapproachintheadaptationframework,werefertopredictivecontrol,whichisbecomingmoreandmorepopularinNCSsnowadays.Indata-basedormodel-basedpre-dictivecontrol,wecanobtainafinitenumberoffuturecontrolcommandsbesidesthecurrentone.Thus,fortheNCSsusingthepredictivecontrolapproach,someofthesequenceofcon-trolcommandsreceivedatthesmartactuatorwillbeappliedtotheplant,dependinguponthepracticaltransmissiondelayandthroughappropriatebufferingandselectionlogics.Theideacanbetracedbackto[36]fortheteleoperationofprestabilizedcon-strainednonlinearsystems.ItisalsothebasisofmorerecentNCSconfigurationsforLTIplantsdescribedin[37]and[38]andthenonlinearplantsconsideredin[24],tonameafew.Theideain[36]isalsoapplicabletotheproblemofnetwork-inducedpacketlosses,andweshallreviewthosereferencesinthenextsubsection.

Althoughtheadaptationframeworkfullyconsidersthespe-cialtiesofNCSs,whichcanreducetheconservatismintheanal-ysisandthedesignofthesystem,therobustnessframeworkismoreapplicabletosomecases,e.g.,whenthetimedelaysareapproximatelyconstant,thepacketsizeiscompressedtosavebandwidth(onlineselectionisimpossible).

TableIliststhereferencesaddressingtheconstraintofnet-work-induceddelayinthetwoframeworks.B.PacketLossesandDisorder

Thereferencesfornetwork-induceddelaysissueareclassi-fiedaccordingtowhetherthemethodologyisdependentonthe

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Fig.5.Severaltypicalimplementationschemesofcontrolinputsatreceiversitestohandlepacketlossesanddisorder.In(a),describestherandompacketlossessubjecttoBernoullidistribution.Thecontrollergainsmaybedesignedofflinein(b),butthecontrollergainsareswitchedandselectedonline.In(c),thecontrolcommandswillbereplacedbytheonespredictedinlatestsuccessfullytransmittedpacket.In(d),adeadlineshouldbesetforthearrivalofthepastpacketforthecontrollertoincludethedelayedsystemstateforperformancebenefitsifany.Notethattheoperationsin(a)–(d)shouldbeclockdriven.

delayinformationonlineornot.ThesamelineofthinkingisalsoapplicabletothecontextofpacketlossesprobleminNCSs.Theobservationsonthedifferenceofcountingthepacketlossesonlineorofflinetodevelopcontrolalgorithmshaveguidedusincategorizingthereferencesintotwoframeworks.Belowweshallfirstreviewthereferencesaddressingthepacketlosses,thenthosethatconsiderbothnetwork-induceddelaysandpacketlosses.Wedeferthereviewofthestudiescombiningdelays,packetlosses,andothertypesofconstraintstolatersubsections.

OneframeworkfortheanalysisanddesignofNCSswithpacketlossesistheofflineframework,wherethecontrollerisde-signeddespiteanysituationofrealpacketlosses.Forinstance,givenanupperboundofconsecutivepacketlosses,thesuf-ficientconditionsderivedofflineinYueetal.[42]ensuretheexistenceofastabilizingcontroller.Theuniquecontrollergainisefficientwhateverthesituationofrealpacketlossesis,aslongasthenumberofconsecutivepacketlossesislessthan.Sim-ilartreatmentscanbefoundin[43].Intheapproach,thecon-troller(oractuator)doesnotneedabuffertostorethepreviousmeasurement(orcontrolinput)anddoesnotneedtojudgeifapacketislostornotonlineandthereforecanbeeventdriven.Anotherapproachintheframeworkistointroducesomestatis-ticsoftherandompacketlosses.In[44],thepacketlossesaremodeledasalinearfunctionofastochasticvariablesatisfyingBernoullirandombinarydistribution.Intheapproach,thesta-bilityofthecorrespondingclosed-loopsystemisdescribedinastochasticsense.Specifically,considerthediscrete-timeNCS

Thus,wehave.Furthermore,introduce

with.Then,anotherBernoulliprocess

onlywhenand,andwehave

otherwise.Therefore

theclosed-loopsystemisgivenby

thepacketdropoutsinbothfeedbackchannelandforwardchannelcanbemodeledviaastochasticprocess,thatis

whereandareindependentBernoulliprocesses.

modelsthepacketlossphenomenonfortheTheprocess

fortheforwardchannel.Also,feedbackchannel,and

anddenotethesuccessandfailure

inthepackettransmission,respectively,whichalsoholdsfor

.Itisassumedthatandobeythefol-lowingprobabilitydistribution:

Thecontroldesignisthencarriedoutbyusingtheexpectation

ofthestochasticvariable.Anothertypicalworkalongthislineis[45].Takingaprobabilityapproachtomodelpacketlossescanalsobeseeninanearlierwork[30],wherethetransmissionrateisproposedtoregardthenetworkwithpacketlossesasaswitchthatclosesatacertainrate.Afurtherexampleisthere-centwork[46],wherethecontrollerdesigntoleratesalargedropprobabilitytoensurethesystemstabilityinthemean-squaresense.Intheapproach,therunningmodeatreceiversshouldbeclockdriven,andtheplantoutput(orcontrolinput)isassumedtobezero[55]orheldatthepreviousvalue[30](byzero-order-holder(ZOH))duringtheperiodsofpacketlosses.Theregener-allyexistsatradeoffbetweenmaximizingthenumberofconsec-utivepacketlosses,maximizingtheallowableprobabilityofpacketlosses,orloweringthetransmissionrateandincreasingthestabilitymarginsand/orsystemperformance.TheschemeoftheapproachisillustratedinFig.5(a).Itcanbeseenthatthecontrollersobtainedofflineareactuallyrobustoverthepacketlosses.

Thesecondframeworkthatwedefinehereisthatthecon-trolinputtoplantsisimplementedonlineaccordingtothesit-uationwhetherapacketislostornot,eventhoughthecon-trollergainsarecomputedoffline.Torealizethis,theintelli-genceofcheckingandcomparingtheindicesofpacketshavetobeequippedwiththeactuator,andtheintelligencerequiretherunningmodeofreceiverstobetimedriven.Atypicalap-proachintheframeworkistoextendtheBernoulliprocessesde-scriptionofthepacketlossesandfurthermodelthecorrelationbetweenpacketlossandnopacketlossasatwo-dimensionalMarkovchain,andthereforethecorrespondingclosed-loopsys-temsasaMarkovjumpsystem[6],[35].Althoughinthesystemthegainsofthetwocontrollerscanbeobtainedoffline,thecon-trolinputswillbeimplementedonlinedependingonwhether

ZHANGetal.:NETWORK-INDUCEDCONSTRAINTSINNETWORKEDCONTROLSYSTEMS—ASURVEY409

apacketislostornot.Aswecommentedinthelastsubsec-tion,theapproachofusingtheMarkovjumpsystemscanbere-placedbynondeterministicswitchedsystemssuchasdescribedin[41].Inthisapproach,thepreviousacceptedmeasuresorcon-trolinputswillbecontinuouslyusedifthecurrentpacketislost.TheschemeisillustratedinFig.5(b).Anothertypicalapproachintheframeworkispredictivecontrolmethodology.Thenat-uralpropertyofpredictivecontrolisthatitcanpredictafinitehorizonoffuturecontrolinputsateachtimeinstant.Thus,ifsomeconsecutivepackets(butwithinthehorizon)afterasuc-cessfulpackettransmissionarelost,thecontrolinputstotheplantcanbesuccessivelyreplacedbythecorrespondingonespredictedinthatsuccessfullyusedpacket.Theideanecessitatesabufferwithmorethanonestorageunit(thelengthisthepredic-tionhorizon)andtheactuatorsitetobeequippedwithselectionintelligence.Fig.5(c)illustratestheapproach.Therepresenta-tiveworksinthislinecanbefoundin[47].Specifically,consideradiscretizednonlinearMIMOplant:

wheretheplantinputs,theplantstates

,andtheuncertaindisturbancebelongstoacompactset,

Thepacketdropoutismodeledbyin

ifthepacketislostatinstant

otherwise.

arecomputedbyThepredictivecontrollercommands

minimizingaperformanceindexateachsampletime:Consideringthepacketlossescase,thecontrolinputis

where

...

.........

...

with

Itcanalsobewrittenvia

if

ifif...ifand,where

and

and

...

Notethatalthoughthepredictedcontrolinputsinasuccess-fullytransmittedpacketarebasedontheplantinopen-loop,

studieshaveshownthatimplementingcontrolinputsinsuchawaywillingeneralresultinabetterperformancethantheap-proachwhereonlythelastusedcontrolinputiskeptandusedinthepresenceoflaterpacketlosses.Itcanbeconcludedfromthetwoabove-reviewedapproachesthatthecontrolinputtothe

plantisselectedfinallyattheactuatorsiteaccordingtowhethertherealpackettransmissionsucceedornot,andthereforeitisonlineandcanbeviewedanadaptationoverpacketlosses.Thestudiesonthepacketdisorderproblemaresporadicsinceinmostliteraturewhatisknownaspastpacketsrejectionlogiciscommonlyemployed,whichmeansthattheolderpacketswillbediscardedifthemostrecentpacketarrivesatreceivers.Thislogiccanbeeasilyrealizedbyembeddingsomeintelligenceatthecontrollersand/ortheactuatorsforcomparison,checking,andselection.Bythelogic,thepacketdisordercanbeviewedaspacketlossesintheanalysisanddesign.However,itshouldbenotedthatthediscardisahumanmadebehavioratreceiversites,whichessentiallydiffersfromtherealpacketlosses.Intheformer,theinformationcarriedinthepastpacketsstillcomesalthoughitisnotfresh.Therefore,akeypointinthepacketdis-orderproblemshouldbewhethertheinformationisusefultothecontroldesign,andifpositive,thepastpacketsrejectionlogicisbetterifitisnotused.In[56],Richardlistshowtousethede-layedsystemstatesinthecontroldesignasanopenproblemintime-delaysystems.Someworkshavealsoshownthattheincor-porationofthepaststateswillimprovethesystemperformancetosomeextent,e.g.,[57].Therefore,if,insomeapplications,someimprovementinsystemperformanceisseriouslyrequired,thepastsystemstateatthecontrollersite,orthepastcontrolin-putsattheactuatorsite,arebetterifused.Toenablethis,anap-propriatetimelinewithinonecontrolperiodshouldbeavailabletomarkthearrivalsofthepastpacketsatthereceivers,i.e.,theyshouldbeclockdriven.AnillustrationisshowninFig.5(d).Iftheuseofthepastinformationdoesnotresultinanappreciableincreaseinperformanceoriftheclock-drivenschemeislimited,thepacketdisorderproblemhastobesolvedsimplythroughthepastpacketsrejectionlogic.Furtherdiscussionsonpacketdis-ordercanbefoundin[48].

Thetypicalworksthatsimultaneouslyaddressbothnetwork-induceddelaysandpacketlossesare[49]–[].In[50],LiandChow,etal.consideranevent-drivencontroller(thegainscanbecomputedoffline)andaclock-drivenactuatorinthesystem.Assumingdifferentscenariosofbothtimedelaysandpacketlossesattheactuatornodes,theclosed-loopsystemismodeledasaswitchedsystem.Thecontrollergainsarethenoptimizedtoensureacertainperformanceofthesystem,andthecontrolcommandsareselectedonlineattheactuatornodeaccordingtotherealsituationofdelaysandpacketlosses.Amongthelit-eraturethatadoptpredictivecontrolmethodologies,Liuetal.[58]considersbothtimedelayandpacketlossesinboththefeedbackandtheforwardchannelsandmodelstheclosed-loopsystemasaswitchedsystem.Thestabilityanalysisofthesys-temsiscarriedoutbyconstructingacommonLyapunovfunc-tion.Thecontrolcommandsareimplementedonlineattheac-tuatornode.Otherexamplestoliteraturethatusethepredictivecontrolapproachforhandlingbothnetwork-inducedconstraintsare[23]an[59].AnotherworkthatconsidersonlineselectionofcontrolcommandsfortheNCSswithbothdelaysandpacketlossesis[52],wherecleartimelinesaresetatthesmartactuatorforonlinechecking,etc.Ontheotherhand,in[49],theauthorsconsiderofflinecontroldesignforNCSswithbothdelaysandpacketlosses,auniquestate-feedbackcontrollergainisused,whichisrobustovertheboundeddelaysandpacketlosses.ByincludingaspecialZOHlogicattheactuatornode,XiongandLam[]mergethetwoconstraintsandmodelthesystemasan

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TABLEII

TYPICALREFERENCESWITHRESPECTTOPACKETLOSSESANDDISORDER

TABLEIII

TYPICALREFERENCESWITHRESPECTTOTIME-VARYINGTRANSMISSIONINTERVALS

inputdelaysystem.Sufficientconditionscontainingtheupperboundoftheinputdelayarederivedsuchthatthesystemissta-bilizedbyanofflinestate-feedbackcontroller.In[51],theauthorproposestwoarchitecturesforoptimalstateestimationofNCSssubjecttobothrandomdelayandpacketlosses.Theestimatorwithconstantgains,anditsimprovedonewithasmartsensorcapableofdatapreprocessing,areobtained.Theproblemofnet-workedidentificationproblemforlinearsystemsisstudiedby[53],whereofflineidentificationalgorithmsaredevelopedcon-sideringNCSswithbothtime-varyingdelaysandpacketlosses.InTableII,wetabulatethetypicalreferencesthataddressonpacketdropoutsanddisorderandalsolistthosesimultaneouslyaddressingbothnetwork-induceddelaysandpacketlosses.Thereferencesthatconsideringadditionaltypesofnetwork-inducedimperfectionswillbepresentedinSectionIII-C(TableIII).C.Time-VaryingSamplingTimes

Inclassicalsampled-datacontrolsystems,thetime-varyingsamplingproblemhasbeenamajortopicofstudyforafewdecades.Inrecentyears,theinterestinthistopichasgrown,motivatedbytheincreasinguseofNCSs,wherethesampledplantoutputsaretransmittedatinstantsthatmayvarysignif-icantlyduetocontentionofmultiplepackets.Here,weshallfirstreviewsomeresultsontime-varyingsamplingprobleminclassicaldigitalcontrolsystems,thenthosethatconsidertheprobleminNCSsenvironment,andfinallytheworksthatsimul-taneouslyaddressothertypesofnetwork-inducedconstraints.Motivationstostudytime-varyingsamplingintervalsindig-italfeedbackcontrolcanbefoundin[60]–[62]andtheclassicaltextbooksonthesubject.In[60],ageneralnonlinearclosed-loopdigitalcontrolsystemwithtime-varyingsamplingiscon-sideredas

Inthemodel,denotesthesamplingpoint,and

meansthetime-varyingsamplinginterval.Thetime-varyingsamplinginstantsareclassifiedintotwocases:fixedornotfixed.Thelattercaseimpliesthatthesamplinginstantsmayvarywithtime,systemstates,orbecontrolledbyanexternalsupervisor.Forbothcases,sufficientconditionsensuringthestabilityof

theclosed-loopsystemareobtained,whereitisrequiredthatthetime-varyingsamplingintervalsshouldbeupperbounded.Inaddition,theinputdelayapproachwasconsideredin[62],wherebysetting

thesampled-datacontrolsystemswithtime-varyingsamplingareequivalentlytransformedtoaninputdelaysystem,

TheLMI-basedcriteriaofthestabilityandcontrolfortheunderlyingsystemsareaccordinglyderived,whichconsistoftheupperbound(canbeoptimized)ofthetime-varyingsam-plingintervals.Othertypicalworksthatconsidertime-varyingsamplingcanbefoundin[71]anditsreferences.

InthecontextofNCSs,thesamplingintervalsare(prefer-ably)termedastransmissionintervals.Withouttheinvolvementofanyoftheothernetwork-inducedimperfections,Zhang[63]proposestheconceptofthetime-varyingtransmissionintervalsexplicitlyandstudiesthestabilityofthecorrespondingNCSs.BasedonaLyapunov-likefunctionwhichcanincreaseduringthetransmissionintervalsbutdecreasesatthetransmissionin-stants,thesufficientconditionscontainingtheupperboundofthetransmissionintervalsareobtained.Anumericalalgorithmisalsodevelopedtofindthebound.Furtherdetailsontheap-proachcanbefoundin[30].Theproblemoftime-varyingtrans-missioninstantsisstudiedinamodel-basedNCSsarchitec-turethatwasproposedin[]and[65].Aimingatreductionintheuseofthenetworkbandwidthinthecontroloflinearsystemsovernetworksfromsensortocontroller,MontestruqueandAntsaklis[]includeanapproximatemodeloftheplantatthecontrollersite,wherethetransmissionintervalsareas-sumedtobeconstant.Inthesetting,thecontrolinputiscal-culated,basedonthestateofthemodelratherthantheoneofplant,andatthesamplinginstantsthestateofmodelisupdatedbythetrueplantstatetransmittedoverthenetwork.Theau-thorsexpandtheirworkin[65],andtwocasesofvariationswithstochasticandnon-stochasticprocessdescriptionsarestudied.ByLyapunovtechniques,thestabilityanalysisofthesystemsarefirstcarriedoutwithoutstochasticknowledgeofthetrans-missiontimesbutwithalowerandanupperboundontrans-missionintervals.Further,assumingthatthetransmissiontimesareindependentandidenticallydistributed(i.i.d.),orarecor-relatedbyaMarkovchain,thestabilityanalysisinalmostsuresenseormean-squaresenseisconducted,respectively.Compar-isonsshowthatthestochasticknowledgeavailsthefindingofthelargerallowablemaximaltransmissioninterval(MATI).Weomittheformulashereandreferthereadersto[14]forthere-viewofthemethodologieswithinthemodel-basedarchitecture.Forthosereferencesthataddresstime-varyingsam-pling/transmissionintervalsandothertypesofnetwork-in-ducedconstraints,wecite[66]–[70]asrepresentativeworks.In[67],thetime-varyingsamplingintervalandadelaylessthanonesamplingintervalarebothconsideredandtime-varyingobserversandstate-feedbackcontrollersaredesignedbasedonLMIgriddingtechniques.HetelandDaffouzetal.[66]considerthesampled-datacontrolsystemswithtime-varyingsamplingintervalsandtime-varyingdelayswhichmaybelargerthanonesamplinginterval.Theoriginalsystemcanbetransformedtoan

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TABLEIV

TYPICALREFERENCESWITHRESPECTTOSCHEDULINGOFNCSS

event-baseddiscrete-timemodel,uponwhichthestabilizabilityofthesystemisachievedbyfindingacontrolforaswitchedpolytopicsystemwithanadditivenormboundeduncertainty.WouwandNaghshtabrizietal.[68]considerbothtime-varyingsamplingintervalsandtime-varyingdelays(mayalsoexceedonesamplinginterval)andstudythetrackingcontrolproblemforthecorrespondingsystem.In[69],Cloostermanetal.studyNCSswithtime-varyingsamplingintervals,time-varyingdelays,andconsecutivepacketlossesbyassumingthattheyarebounded.Also,basedonmodel-basedNCSsarchitecture,Polushin,Liuetal.[70]furtherconsidernonlinearsystems,time-varyingsamplingintervals,andunknowntime-varyingdelaysinbothfeedbackchannelandforwardchannel,packetlosses,andclockasynchronizationconstraints.Aspecificprotocolisproposedthereforthesystemtodealwiththeconstraints.Itisworthnotingthattherearequiteanumberofreferencesconsideringthesimultaneousexistenceofbothcompetitionofnodesandtime-varyingsamplingintervalsinNCSs,sincethelatterconstraintismainlycausedbytheformer.TightrelationsexistbetweentheMATIandcertainnetworkprotocolstocopewithcompetitionofnetworknodes.WeshallelaborateontherelationsinSectionIII-D.

TableIIIliststhetypicalreferencesaddressingtime-varyingsamplingintervalsinclassicaldigitalcontroltheories,thestudiesontheprobleminNCSs,andthosereferencessi-multaneouslyconsideringothertypesofnetwork-inducedimperfections(thecasewithcompetitionofnodeswillbeshowninTableIV).

D.CompetitionofNodesAccessingNetwork

InNCSs,thenetworkmaybealsosharedbyothercontrolloopsordatacommunicationtasks.Thecompetitionofnetworknodesaccessingnetworksisunavoidable.Infact,evenforthescenarioofonlyonepackettransmissioninthecontrolloop,i.e.,thenetworknodesareonlyonesensor,oneactuatorandonecontroller,thecompetitionmayoccurbetweenthesensornodereportingthemeasuresandtheactuatornodeexecutingthecontrolinputswhenthefeedbackandtheforwardchan-nelsarebothnetworked.Withoutanyschedulingpolicy,theresultingnetworkcongestion,whichessentiallyleadstothoseunanticipatedphenomenasuchasnetworkaccessingdelaysandpacketlosses,maybeveryserious.Howtoorchestratethetrans-missionsofthemultiplepackets,i.e.,theschedulingprotocol,shouldbedesignedgracefullyaswellasthosecontrolmethod-ologiesovercomingtheimpactsofothernetwork-inducedim-perfections.Notethatthecongestionproblemmaybepartiallysolvedbyresortingtotheinformationtheoreticaltools;how-ever,ithasbeenwellrecognized,(e.g.,in[28])thatthebene-fitsarenotnotable.ItisthereforemoresignificantfromcontrolperspectivestoequipthenodesofanNCSwithschedulersandcalculatethedeadlinesforpackettransmissionintervals.Here,

weshallreviewtherepresentativeworksinthisregardfirstandthereferencesconsideringtheschedulingprobleminthesimul-taneouspresenceofothertypesofnetwork-inducedconstraints.Weareonlyconcernedwiththesituationofmultiplenodesinacontrolloopconstructedoveracertainnetwork.

Firstofall,thecompetitionofmultiplenodesaccessingnet-workscanbeillustratedinFig.6,wheretwosensornodesofplantoutputandonecontrollernodeofcontrolinputaccessthenetworkalternatelyorinsomedynamicway,1andonlyonenodeisallowedtotransmititspacketpertransmission.Itcanbede-ducedfromFig.6that,iftheprotocoldeterminingwhichnodesaccessnetworkisdifferent,thentheerrorsbetweentheoriginalsignals(eithercontrolinputand/ormeasuredoutput)

andtheirnetworkedversionswillbe

different.Theerrors

canbecallednetwork-inducederrorandtightlyrelatetothestabilityandperformance

oftheclosed-loopsystem.InFig.3,

arethetransmis-sioninstantsand

arethetransmissiondelays.Bythedenotations,theMATIisdefinedas

andthemaximumallowabledelaybound(MADB)isdefinedas

.Therefore,differentdeadlinesofthepacket

transmissionintervals(i.e.,MATI)arerequiredfordifferentprotocols.Earlierworksalongtheresearchlinecanbetypicallyfoundin[28].Intheworks,withoutconsideringnetwork-in-duceddelays

,thetwoschedulingstrategies,i.e.,thetry-once-discard(TOD)andthetoken-ring-typesched-uling,werestudied.Theformerisdynamicwithamaximum-error-first(MEF)schedulingpolicy,implyingthatthenodewiththegreatestweightederrorfromitslastreportedvaluewillbegrantedaccesstonetwork.Thetoken-ring-typescheduling,alsocalledround-robin(RR)scheduling,isastaticone,bywhicheachnodeaccessesthenetworkalternatelyinafixedorder.Forbothstaticanddynamicscheduling,thedifferentMATIboundsarerigorouslycalculated,respectively,ensuringthatthesystemisgloballyexponentialstable.Notethatthecontrolledplantin[28]isconsideredtobelinear,andthestabilizingcontrollerisdesignedaprioriwithoutthenetworkincludedintotheloop.Alinearizedmodelofunstablebatchreactor(hasbecomeabenchmarkalongthisresearchline)wasusedtoverifythere-sults.Consideringnonlinearplantswithexternaldisturbances,NesicandTeelfurtherextendedthestaticanddynamicproto-colsstudiedin[28]tothemoregeneralclassofuniformlyglob-allyexponentiallystable(UGES)protocols.Theinput–outputandtheinput-statestabilityanalysisarecarriedoutin[72]and[73],respectively,andtheboundofMATIensuringthesystemstabilityisimproved.In[74],thelargerMATIboundisfur-therobtainedwithsimpleprooffortheinput–outputstabilityproblem.In[75],theproblemisexplicitlyconsideredforwire-lesschannels.Notethatalltheworksin[72]–[75]assumethatastabilizingcontrollerintheabsenceofnetworksisdesignablefortheplant.In[76],theco-designoftheschedulingprotocolandcontrollerwasstudiedforlinearplants.ByLMItechniques,

1Note

thatthedynamicschedulingmaybetime-dependentorstate-depen-dent,orgovernedbyexternalfactors.

412IEEETRANSACTIONSONINDUSTRIALINFORMATICS,VOL.9,NO.1,FEBRUARY2013

Fig.6.Illustrationofcompetitionofthreenodes(twosensornodesandonecontrollernode)accessingnetwork.(a)Thealternatemanner.(b)Somedynamicmanner.isthetransmissiondelayaftertransmissioninstant.

thedynamicoutputfeedbackcontrollerisdesignedsuchthatthesystemisquadraticallystablewithalargerMATIboundusingthecommunicationprotocolbelongingtotheTODprotocols.Consideringagroupoflineartime-invariantplantscon-trolledoverasharednetwork,i.e.,multiplecontrolloops,DaiandLinetal.[82]studiedtheschedulingandcontrolcodesignproblemoftheunderlyingNCSsinthepresenceofuncertaintimedelaysbyusingswitchedsystemsapproach.In[77],theschedulingproblemandtime-delayphenomenaarebothtakenintoaccount;theLMI-basedconditions,togetherwiththeso-calledearliestdeadlinefirst(EDF)algorithm,ensurethesystemstabilityforanytime-delayboundedbyMADB.Basedon[72]andanalysiswithrespecttotherealEthernetandEthernet-likeprotocols,TabbaraandNesic[79]furtherconsideredthestochasticschedulingprotocolsandstochasticpacketdropouts.Detailedcomparisonsbetweentheproposedstochasticprotocolsandthedeterministicprotocols,e.g.,theUGESprotocolsstudiedin[72],aregiven,assumingtherandompacketsoccur.In[78],viaProfibustokenpassingpro-tocol,theQoS-basedremotecontrolofanNCSisinvestigatedsimultaneouslytakingtherandombutboundednetworkdelays(affectedbythecertainprotocolparameters)intoaccount.In[80],thenetwork-inducedconstraints,time-varyingsampling,

),packetlosses,time-varyingdelays(assuming

andthecompetitionofnodesaccessingnetworksareconsid-ered.AhybridsystemframeworkfortheunderlyingNCSsisestablishedbyintroducingaseriesofdefinitions,includinghybridtimedomain,andhybridtrajectory,andseveralstabilityanalysesarecarriedout,suchasUGAS,UGES,USPAS,stability.In[81],theswitchedsystemsapproachisusedtomodelthesystemwiththeprotocolastheswitchingfunction.TheTODprotocolandRRprotocolisgeneralizedasaquadraticprotocolandaperiodicprotocol,respectively.ThestabilityproblemoftheNCSinlinearcontextisinvestigatedbyusingtechniquesofconvexoverapproximationandLMIs.

ThetypicalreferenceswithrespecttostudiesontheissuesofschedulingofNCSsareshowninTableIV.E.Quantization

Thediscussionsonquantizationproblemscanbefoundintextbooksoncomputer/digitalcontroltheories,e.g.,[83].Theimpactofquantization,similartononlinearitiesinthesystem,willleadthecontrolledoutputtobehaviorssuchaslimitcircle,dead-zone,andchaos.Thecontrollaws,developedbyassuming

thatthedatatransmissionrequiredbythesystemcanbeper-formedwithinfiniteprecision,maynotbevalidinthepresenceofsignalquantization.Therefore,thereisaneedfordevelopingtoolsforanalysisanddesignofquantizedfeedbacksystems,andmanyimportantresultshavebeenreported.

Amongtheseresults,therearemainlytwoapproaches.Thefirstoneconsidersmemorylessfeedbackquantizers,whicharealsotermedasstaticquantizationpolicies,e.g.,[86]–[].Con-sideralineardiscrete-timesystemwithastate-feedbackcon-trollergain

whereisthequantizedcontrolinputandisthequantizer.Itispresumedinsuchstaticpoliciesthatdataquan-tizationattimeisdependentonthedataattimeonly,whichleadstorelativelysimplestructuresforthecoding/decodingschemes.ThefirstmathematicaltreatmentofcontrolsystemswithuniformquantizedfeedbackwasgiveninDelchamps[86],followingwhichthepropositionthataboundonthenumberofquantizationintervalsisneededtostabilizealinearsystemwasgivenin[87].EliaandMitter[88]consideredtheproblemofquadraticstabilizationfordiscrete-timesingle-inputsingle-output(SISO)lineartime-invariantsystems;itisproventhatforaquadraticallystabilizablesystem,thequantizerneedstobelogarithmic.Followingthiswork,FuandXie[]usedthesectorboundapproachtoquantizedfeedbackcontrol,gaveacomprehensivestudyonfeedbackcontrolsystemswithlogarithmicquantizers,andpresentedcompleteresultsforbothSISOandmultiple-inputmultiple-output(MIMO)lineardiscrete-timesystems.Inaddition,controlperformanceissues,

control,weretreatedincludingguaranteedcostcontroland

inaunifiedframework.

Thesecondapproachusesaclassofdynamic(ortime-varying)quantizersthatdynamicallyscalesthequan-tizationlevelsaccordingtothelocationofthestate.TheapproachwasproposedbyBrockettandLiberzonin[84]and[85].Supposethatalineardiscrete-timesystem,withastate-feedbackcontrollergain,

ZHANGetal.:NETWORK-INDUCEDCONSTRAINTSINNETWORKEDCONTROLSYSTEMS—ASURVEY413

whereisthequantizedcontrolinputandisthe

dynamicalquantizerdependingonafunctionoftime.Aseriesofworksarecarriedouttodifferentscenariossuchasthetreatmentofbothinputandoutputquantizationin[85],con-sideringexogenousdisturbancesinthequantizedcontrolsys-temsin[96],andthenonlinearsystemsmodelsin[97].Assum-marizedbyNesicandLiberzonin[95],regardingthequanti-zationalgorithmsassomeprotocolsaswell,thequantizationcanbeclassifiedastwotypes—the“box”protocols[97]andthe“zoom”protocols[96]—bywhichaunifiedframeworkisbuiltin[95]forthedesignofNCSswithsimultaneousexistenceoftheschedulingofnetworknodesandthequantizationofsystemstate.

Inadditiontotheadvancesinthefieldofquantizedcontrolitself,thenetwork-basedcontrolalsostimulatestherenascenceofstudiesonquantization.AlthoughthequantizationeffectsbecomemoreandmorenegligibleinmanyNCSs,thestudieswillbeespeciallyhelpfultothesituationwhereonlyasmallnumberofbits(shorterwordlength)canberealizedorthesizeofthetransmittedpacketsispreferablyreducedforadesiredallocationofnetworkbandwidth.Suchexpectationsmotivatedthestudiesonthesimultaneousexistenceofquantizationphe-nomenaandothernetwork-inducedimperfections.

Thetypicalworksaddressingbothdelaysandquantizationcanbefoundin[90]and[91].UsingtheRazumikhinapproachandsmall-gainarguments,in[90],aninput-to-statestabilizingfeedbackcontrolisdesignedinthepresenceofconstantdelayandquantization(dynamic)suchthatthesystemstateremainboundedandeventuallyenterasmallerregionthantheinitialregion.FridmanandDambrine[91]consideredatime-varyingdelayandstaticquantizationandusedtheLyapunov–Krasovskiifunctionmethod,bywhichtheLMI-basedconditionsforthecontrollersdesignareobtainedsuchthatthesystemstatealsoconvergestoaboundedregion.Thesaturationproblemisalsoaddressedin[91].

ThestabilityanalysisofNCSstakingbothpacketdropoutsandfinite-levelstaticquantizationofcontrolsignalsintoac-countisconducted,ineitherastochasticsetting[92]orade-terministicsetting[93].Theworkreportedin[93]isbasedon

theprimaryresultsobtainedin[47]andemploysaweaker

tostabilitynotion.Thetradeoffbetweenpacketdropoutsandquantization,andthetradeoffbetweenthedisturbanceattenua-tionandthemaximumnumberofconsecutivepacketdropoutsandthestepsizeofthequantizer,areestablishedin[92]and[93],respectively.

Complementingtheworkreportedin[31],TianandYueetal.[94]simultaneouslyconsiderthenetwork-induceddelaysofbothsensortocontrollerandcontrollertoactuator,andthequan-tizationofbothcontrolandstatesignals,packetsdropoutsinthesystemmodel.LMItechniquesareusedforthesolutionsofoutputfeedbackcontrolthere.GaoandChen[43]alsoconsid-eredthequantization,packetdropout,anddelayissuestogether,

andinvestigatedtheproblemof

trackingcontrolforcon-tinuous-timeNCSs.There,thequantizationproblemishandledusinganlogarithmicquantizerbasedon[].

Basedonthework[72]forschedulingissueofNCSsandtheworksforquantizedfeedbackcontrol[85],[96],[97],aunifiedframeworkforstudyingtheproblemsofschedulingandquan-tizationinNCSsisproposedbyNesicandLiberzonin[95]afterexposingtheinherentsimilaritiesoftreatingscheduling

TABLEV

TYPICALREFERENCESWITHRESPECTTOQUANTIZATION

problemofNCSsandquantizedcontrolproblem.Theproto-colsincludingRRandTODprotocolsin[72]arerevised,re-spectively,totheversionwithquantizationofeither“box”or“zoom”type.Themaindesignstepsthereconsistofthedesignofastabilizingcontrollerwithoutconsideringquantizationandtimescheduling,thedesignoftheMATIensuringthestabilityofthesystemsclosedoveranetworkwithstatequantization.TheMATIiscomputedbyseveralprotocol-dependentparam-etersindicatinghowtheschedulingprotocolsandquantizationstrategiesareselected.

TableVliststherepresentativereferencesaddressingthequantizedcontrolproblemsandco-analysisandco-designofquantizationandothertypesofconstraintsinNCSs.

IV.CONCLUSIONANDFUTUREWORKS

Inthispaper,thestudiesseenintheliteratureonfivetypesofnetwork-inducedconstraintsaremainlysurveyed,includingtimedelays,packetlossesanddisorder,time-varyingtransmis-sionintervals,competitionofmultiplenodeaccessingnetworks,anddataquantization.SectionIIprovidesanoverviewofthesourceofeachnetwork-inducedconstraint,theirnegativeim-pacts,andthecorrespondingresearchlinesinhandlingthem.InSectionIII-A,weclassifythevastreferencesuptodateontimedelaysintotwoframeworks,therobustnessframework,andtheadaptationframework,whichmeansthatthecontroldesignspecificsarerobustoveroradaptivetothedelaysvariations,respectively.SimilarthinkingalsogiverisetocategorizingthereferenceswithrespecttopacketlossesintotwoframeworksinSectionIII-B,theonlineandofflineones.Inaddition,onthepacketdisorderproblem,weproposedanapproachthatdiffersfromthecommonlyusedpastpacketsrejectionlogic.Thewaysofsortingthereferencesonthefirsttwonetwork-inducedconstraintsdistinguishoursurveyfromtheexistingones.Moreexplicitly,wecomplementtheprevioussurveysonthelatterthreetypesofconstraintsinSectionsIII-C–III-E,respectively.Weareawarethatitishardlypossibletocoverallthecontri-butionsinthearea;therefore,ouremphasisisplacedonthecategorizationsofthevastliterature.Theapplicabilityorthelimitationsofthedevelopedapproacheshavenotthoroughlybeencommentedon.Accordingtothecategorizationandthesummarizedresearchlines,onecanresorttoapossiblesolutionthatiscapableofcopingwiththenetwork-inducedconstraintsoncethenetworkisselected.

Despitediverseresults,therearestillnumerouspointsthatshouldbefurtherconsideredinfutureworks.Wehighlightsomeofthemasfollows.

1)Forstudiesusingstochasticprocessestomodelthecon-straints,suchastheMarkovchainfortime-varyingde-laysortime-varyingtransmissionintervals,Bernoullidis-tributionfortime-varyingtransmissionintervalsorpacket

414IEEETRANSACTIONSONINDUSTRIALINFORMATICS,VOL.9,NO.1,FEBRUARY2013

losses,thestatisticsknowledge,e.g.,theusedprobabili-tiesaregenerallyassumedtobecertainorexactlyknown.FurtherinvestigationsonthemodeledNCSsbyuncertainorpartiallyunknownstatisticsknowledge,cf.[98],willbemorepractical.

2)Forthoseapproachescontainingsomeboundedparame-tersthatcancharacterizethenetwork-inducedconstraints,suchastheMADB,MATI,maximalconsecutivepacketlosses,quantizationdensity,anaturalextensiontogoonistofindthebiggerallowableboundforfurtherconser-vatismreductionintheconcernofsystemstabilityandper-formance(whichhasactuallybeenthemainresearchlineinmanyapproaches).

3)Whileitisnotalwaysnecessarytotakeallthenetwork-inducedconstraintsintoaccountintheanalysisandde-signofNCSs(sometechniquesarenotcoupled),itmustbementionedthatthecomprehensivestudiescombingalltheconstraintsarenotsufficientyet,especiallyforap-plyingthetechniquesdevelopedinthesituationofonepackettransmissiontothesituationofmultiplepacketstransmission.Forinstance,ifonesimultaneouslyconsidersthetime-varyingdelaysandthecompetitionofmultiplenodes,theanalysisandsynthesisofNCSswillbemorechallenging,especiallythetime-varyingdelaysarelargerthanonetransmissioninterval.

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LixianZhang(M’10)receivedthePh.D.degreeincontrolscienceandengineeringfromtheHarbinIn-stituteofTechnology,Harbin,China,in2006.

FromJanuary2007toSeptember2008,heworkedasaPostdoctoralFellowintheDepartmentofMechanicalEngineeringatEcolePolytechniquedeMontreal,QC,Canada.HewasaSino-BritishFellowshipTrustVisitorinTheUniversityoffromJuly2009toOctober2009.InJanuary2009,hejoinedtheHarbinInstituteofTechnology,China,whereheiscurrentlyanAssociateProfessor

inResearchInstituteofIntelligentControlandSystems.SinceFebruary2012,hehasbeenavisitingscholarattheProcessSystemsEngineeringLaboratory,MassachusettsInstituteofTechnology(MIT),Cambridge.Hisresearchin-terestsincludenondeterministicandstochasticswitchedsystems,networkedcontrolsystemsandtheirapplications.

Dr.ZhangservesasanAssociatedEditorforvariouspeer-reviewedjournals,includingtheIEEETRANSACTIONSONSYSTEMSMANANDCYBERNETICS—PARTB:CYBERNETICS.

HuijunGao(SM’09)receivedthePh.D.degreeincontrolscienceandengineeringfromtheHarbinIn-stituteofTechnology,Harbin,China,in2005.

HewasaResearchAssociatewiththeDepartmentofMechanicalEngineering,TheUniversityof,fromNovember2003toAugust2004.FromOctober2005toOctober2007,heconductedhispostdoctoralresearchwiththeDepartmentofElectricalandComputerEngineering,UniversityofAlberta,AB,Canada.SinceNovember2004,hehasbeenwiththeHarbinInstituteofTechnology,

whereheiscurrentlyaProfessorandDirectoroftheResearchInstituteofIntelligentControlandSystems.Hisresearchinterestsincludenetwork-basedcontrol,robustcontrol/filtertheory,time-delaysystems,andtheirengineeringapplications.

Dr.GaoisanAssociateEditorforsuchpublicationsasAutomatica,theIEEETRANSACTIONSONINDUSTRIALELECTRONICS,theIEEETRANSACTIONSONSYSTEMS,MAN,ANDCYBERNETICS—PARTB:CYBERNETICS,theIEEETRANSACTIONSONFUZZYSYSTEMS,theIEEETRANSACTIONSONCIRCUITSANDSYSTEMS—PARTI,andtheIEEETRANSACTIONSONCONTROLSYSTEMSTECHNOLOGY.

OkyayKaynak(SM’90–F’03)receivedthePh.D.degreeintheDepartmentofElectronicandElectricalEngineeringfromtheUniversityofBirmingham,Birmingham,U.K.,in1972.

From1972to1979,heheldvariouspositionswithintheindustry.In1979,hejoinedtheDe-partmentofElectricalandElectronicsEngineeringBogaziciUniversity,Istanbul,Turkey,whereheiscurrentlyaFullProfessor.HehasservedastheChairmanoftheComputerEngineeringandtheElectricalandElectronicEngineeringDepartments

andastheDirectoroftheBiomedicalEngineeringInstitute,BogaziciUniver-sity.Currently,heistheUNESCOChaironMechatronicsandtheDirectoroftheMechatronicsResearchandApplicationCenter.HehasheldVisitingProfessor/ScholarpositionsatvariousinstitutionsinJapan,Germany,theUnitedStates,andSingapore.Hiscurrentresearchinterestsareinthefieldsofintelligentcontrolandmechatronics.Hehasauthoredthreebooksandeditedfivebooksandauthoredorcoauthoredmorethan300papersthathaveappearedinvariousjournalsandconferenceproceedings.

Dr.KaynakisservingorhasservedontheEditorialorAdvisoryBoardsofanumberofscholarlyjournals.Currently,heisaCo-Editor-in-ChiefoftheIEEETRANSACTIONSONINDUSTRIALELECTRONICSandanAssociateEditoroftheIEEESENSORSJOURNALandtheIEEE/ASMETRANSACTIONSONMECHATRONICS.Heisactiveininternationallyorganizations,hasservedonmanycommitteesoftheIEEE,andwasthePresidentoftheIEEEIndustrialElectronicsSocietyduring2002–2003andVice-President(forConferences)ofComputationalIntelligenceSocietyduring2004–2005.