何谓混杂系统

WhatIsaHybridSystem?JanLunzeInstituteofAutomationandComputerControlRuhr-UniversityBochumUniversitätsstraße150D-44780Bochumphone:[phone](Aluretal.,1996,Antsaklisetal.,1999,Antsaklisetal.,1995,Antsaklisetal.,1997,Grossmanetal.,1993,LynchandKrogh,2000),thespecialjournalissues(AntsaklisandNerode,1998a,DEDS’98,1998)and(Automatica35(3),1999)andthisbookdescribethedifferentresearchdirectionsandresultsobtained.Thehybridnatureofsuchsystemshasattractedtheinterestofmathematicians,controlengineersandcomputerscientists.Themethodsappliedandtheresultsobtainedareasdiverseasthebackgroundsoftheseresearchers.Nocommondefinitionofahybridsystemisavailable.Amajorargumentinthehybridsystemliteraturesaysthatagivendynamicalsystemshouldbeconsideredahybridsystemif(andonlyif)itisimpossibletodealwithiteitherasapurelycontinuous–variablesystemorasapurelydiscrete–eventsystemwithoutignoringimportantphenomenathatresultfromthecombinationofcontinuousanddiscretemovementsofthissystem.Hereandintherestofthepaper,thetermscontinuousanddiscreteareusedwithrespecttotherangeofthesignalsandnotwithrespecttothetimeoverwhichthesignalsaredefined.Thisargumentdoesnotclarifywhatahybridsystemis.Mostofthetheoreticalpapersstartwithagivenhybridsystemanddonotconsiderwhetherandwhyhybridsystemstheoryhastobeappliedtothesystemunderinvestigation.Likewise,ap-plicationpapersusehybridmodelsandanalysistoolsbutdonotelaboratethemainreasonswhythesystemhadtobedealtwithasahybridsystem.Mostofthechap-tersofthisbookadoptthesamepositionandinvestigatedifferentkindsofhybridsystems.S.Engell,G.Frehse,E.Schnieder(Eds.):Modelling,AnalysisandDesignofHybridSystems,LNCIS279,pp.3−14,2002.Springer-VerlagBerlinHeidelberg20024J.LunzeThissituationisduetothefactthatthetheoriesofcontinuousanddiscretesystemshavebeenelaboratedcompletelyseparatelyuntilrecently.Hybridsystemsposetheproblemofbridgingthegapbetweenboththeories.Thishasbeendoneuntilnownotonlybyconsideringacombinationofcontinuousanddiscretesubsystemsbutalsobyinvestigatingdifferentextensionsofeithercontinuousordiscretesystems.TimedorhybridPetriNetsandtimedautomatageneralisetheuntimedmodelsthataretypicallyusedindiscretesystemstheorywhereasswitchedsystemsextendcontinu-oussystemsbydiscretephenomena,tomentionsomeexamplesystemsinvestigatedinthisbook.Fromatheoreticalpointofviewthedefinitionofthefieldofhybridsystemsbyacollectionofdifferentkindsofsystemsormodelsisnotsatisfactory.Itisimportanttoknowwhythenewclassofhybridsystemshastobedefined,becausethisclarifiesthenoveltyofdynamicalphenomenatobeinvestigatedandthenecessityofdevelopingnewconcepts,methodsandtools.Thischaptergivesananswertothequestionofwhatahybridsystemis.Itarguesthatanewnotionshouldonlybedefinediftheclassofsystemsunderinvestigationdoesnotfallwithintheframeworkofthealreadyexistingtheory.Thecharacterisationofhybridsystemsgivenhereisinsomecontradictionwithdefinitionsusedinliterature.Itshouldinitiateathoroughdiscussionofthisnewnotion.Theproblemofdefiningahybridsystemisratherinvolvedbecauseitisnotthecharacteristicsofagivendynamicalsystemalonethatdistinguishescontinuousfromdiscreteandhybridsystems.Forexample,atanksystemisusuallyconsideredtobecontinuousifalevelcontrolleristobedesignedbutitistackledasadiscretesystemifitisanalysedasapartofabatchprocess,inwhichonlythediscretestateofafulloranemptytankaredistinguished.Theintentionsofmodelling,analysisorcontrolhaveaconsiderableinfluenceonthefactwhetherasystemhastobeconsideredasahybridsystemornot.Hybriddynamicalsystemshaveexistedforlong,butbeforetheappearanceofthecurrentlydevelopingtheoryonhybridsystems,thesesystemshaveeitherbeenconsideredaspurelycontinuousoraspurelydiscrete.Thereasonwhytheybecameahottopicinresearchisgivenbythefactthatmanymoderntechnologicalprocessescannotbeanalysedandcontrolledbyinvestigatingonlythecontinuousoronlythediscretemovements.Asthetheoriesofcontinuousordiscretesystemshavemadecontradictorybasicassumptions,whichhavetobesatisfiedbythesystemsinordertomaketheirrepresentationintheframeworkoftherespectivetheorypossible,theconsiderationofbothcontinuousanddiscretephenomenamakesitnecessarytodevelopanewtheory.Roughlyspeaking,ifthemainassumptionsofboththeoriesarenotsatisfied,asystemhastobedealtwithasahybridsystem.Definition1.Ahybridsystemisadynamicalsystemthatcannotberepresentedandanalysedwithsufficientprecisioneitherbythemethodsofthecontinuoussystemstheoryorbythemethodsofthediscretesystemstheory.WhatIsaHybridSystem?5Remark