Liveness Problem of Petri Nets Supervisory Control Theory for Discrete Event Systems

A quite great progress of the supervisory control theory for discrete event systems (DES) has been made in the past nearly twenty years, and now, automata, formal language and Petri nets become the main research tools. This paper focus on the Petri nets ba

Vol.31,No.1ACTAAUTOMATICASINICAJanuary,2005LivenessProblemofPetriNetsSupervisoryControlTheoryfor

DiscreteEventSystems1)

Hong-YeSUWei-MinWUJianCHU

(NationalLaboratoryofIndustrialControlTechnology&InstituteofAdvancedProcessControl,

ZhejiangUniversity,Hangzhou310027P.R.China)

(E-mail:{hysu,wmwu,chuj}@http://www.wendangwang.com)

AbstractAquitegreatprogressofthesupervisorycontroltheoryfordiscreteeventsystems(DES)hasbeenmadeinthepastnearlytwentyyears,andnow,automata,formallanguageandPetrinetsbecomethemainresearchtools.ThispaperfocusonthePetrinetsbasedsupervisorycontroltheoryofDES.Firstly,wereviewtheresearchresultsinthis eld,andclaimthattheregenerallyexistsaprobleminPetrinetsbasedsupervisorycontroltheoryofDES,thatis,thedeadlockcausedbythecontrollerintroducedtoenforcethegivenspeci cationoccursintheclosed-loopsystems,especiallythedeadlockoccursintheclosed-loopsysteminwhichtheoriginalplantislive.Finally,apossibleresearchdirectionispresentedforthesolutionofthisproblem.

KeywordsDiscreteeventsystems,supervisorycontrol,Petrinets,liveness

Introduction

Discreteeventsystem(DES)isanewkindofdynamicalsystemscreatedalongwiththedevelop-mentofcomputerscience,communicationnetworksandsensortechnology.TheprimereasontostudyDEStheoryistherapidlydevelopedhightechnology,aspointedoutbyZhengDazhongandZhengYingping[1].ExamplesofDESincludecomputercommunicationnetworks,automatedmanufacturingsystem,especially exiblemanufacturingsystem(FMS)andcomputerintegratedmanufacturingsystem(CIMS),computercontrolsystem,operationsystem,spacetra ccontrolsystem,militaryC3Isystem,supervisorycontrolsysteminintelligentbuildingandmobiletelephone,intelligenttransportation,dis-tributedsoftwaresystemandsoon.Thesystemsmentionedabovearecontrolledinlargepartbyman-madeoperationrules.Soitsdynamicpropertyisdeterminedbytheeventsrandomlyoccurredatthediscretetimeinstance,andtheclassicalcontroltheorybasedondi erentialordi erenceequationscannotbeusedtoanalyzeandsynthesizeDES.ThemainmathematicmodelofDESisrandomprocessmodelsuchasMarkovchainandsequencetheory,automatonandPetrinets(PN),etc.AutomatonandPNismainlyappliedtosystemsynthesiswhileMarkovchainisusedinperformanceanalysis.

AutomatonandformallanguageareadoptedasthemainresearchtoolsfortheinitialsupervisorycontroltheoryofDESbyRamadgeandWonham,thefounderofthetheory,andreferredasRWtheory[2~5].ThoughtheautomatonandformallanguagemodelofDEShastheadvantagethatitseparatestheconceptofopen-loopdynamics(plant)fromthefeedbackcontrol[4],ithasgreatdi cultyofovercomingcomputationcomplexity,especiallyinthecasethatthecontrolledsystemsisalargesystemconstitutedbymanyinteractingsubsystems.Forexample,ifanautomatedguidedvehiclecoordinationsystemmadeof vevehiclesismodeledbyautomaton,itwouldhavewelloveramillionsystemstates,andthusthecomputationofitsfeedbackcontrolpolicyisnearlyimpossible[6].GiuasummarizedtheadvantagesofPNmodelforsupervisorycontrolofDES[7,8]:

1)PNhasahigherlanguagecomplexitythanautomatonsincePetrinetlanguagesareapropersupersetofregularlanguages;

2)ThestatesofaPNarerepresentedbythepossiblemarkingsandnotbytheplaces,theyallowacompactdescription,i.e.,thestructureofthenetmaybemaintainedsmallinsizeevenifthenumberofthemarkingsgrows;

3)Petrinetsallowmodularsynthesis.

BecausePetrinetshavetheadvantagesofthegraphicalanddistributedrepresentationforthesystemstatesandthecomputationale ciencies,inaddition,theperformancecharacteristicsofPN1

Liveness Problem of Petri Nets Supervisory Control Theory for Discrete Event Systems相关文档

最新文档

返回顶部