1、A goal-based approach for modeling and simulation ofdifferent types of system-of-systemsFENGYimin1,ZHOUChenchu2,ZOUQiang1,*,LIUYusheng1,LYUJiyuan3,and WUXinfeng31.StateKeyLabofCAD&CG,ZhejiangUniversity,Hangzhou310027,China;2.XianAerospacePropulsionInstitute,Xian710100,China;3.ChinaAstronautResearcha
2、ndTrainningCenter,Beijing100094,ChinaAbstract:A system of systems(SoS)composes a set of inde-pendent constituent systems(CSs),where the degree of autho-rity to control the independence of CSs varies,depending on dif-ferent SoS types.Key researchers describe four SoS types withdescending levels of ce
3、ntral authority:directed,acknowledged,collaborative and virtual.Although the definitions have been re-cognized in SoS engineering,what is challenging is the difficultyof translating these definitions into models and simulation envi-ronments.Thus,we provide a goal-based method including amathematical
4、 baseline to translate these definitions into moreeffective agent-based modeling and simulations.First,we con-struct the theoretical models of CS and SoS.Based on the theo-retical models,we analyze the degree of authority influenced bySoS characteristics.Next,we propose a definition of SoS typesby q
5、uantitatively explaining the degree of authority.Finally,werecognize the differences between acknowledged SoS and col-laborative SoS using a migrating waterfowl flock by an agent-based model (ABM)simulation.This paper contributes to theSoS body of knowledge by increasing our understanding of thedegr
6、ee of authority in an SoS,so we may identify suitable SoStypes to achieve SoS goals by modeling and simulation.Keywords:simulation,systems agent-based modeling,systems-of-systems(SoS),systems thinking.DOI:10.23919/JSEE.2023.0000841.IntroductionA system of systems(SoS)comprises a collection ofindepen
7、dentsystemsthatinteroperatetogethertoachieveoverarchingcapabilities1,2.ApplicationsofSoScanbefoundindiversedomains,suchasmilitary1,aerospace3,health care 4,transportation 5,and energy 6,amongothers.Comparedtothetraditionalsysteminthefieldofsystemsengineering(SE),thedevelopmentofanSoSinthefieldofSoSe
8、ngineering(SoSE)ischallengedbyincreasingcomplexityresultsfromtheindependenceofconstituentsystems(CSs)7,8.Thechallengepromptstheneedfortwoaspectsofefforts:analyzingtheindepen-denceofCSsandmodelingmethodsforSoS.Ontheonehand,aseachCShasmanagerialandoperationalinde-pendence9,10,anSoScanbedesignedbyconsi
9、deringfourtypes(archetype,category,classification,typology)based on the degree of authority(managerial control)11.UnderstandingSoStypesisnecessarytoprovideaframeworkforunderstandingSoS1214andsupportsthe development of SoS 1517.On the other hand,model-based systems engineering(MBSE),whichfocusestheSE
10、processonwell-constructedmodelsthatcapturetheessenceofthesystem,canhelpaddressthecomplexityofSoS18,19.Therehasbeenconsiderableinterest in using model-based techniques for SoSE20,21.For effective model-based SoS engineering(MBSoSE),Nielsenetal.8identifieddifferentdimen-sions,oneofwhichisthecategoryof
11、SoS,forposition-inganMBSoSEapproach.TheypointouttheneedforSoStypestoguidethedevelopmentofanSoSbecausethe degree of managerial control determines the adapt-abilityandcollaborationofeachCSintermsofrequire-ments,interfaces,dataformats,andtechnologies8.Inaword,theneedforunderstandingandmodelingSoStypest
12、oenrichSoStheoryandSoSpracticeisapparent.How-ever,theproblemishowtoprovideawell-defineddefini-tionthatcanbetranslatedintomoreeffectivemodelsandsimulationsofSoSs.AbasicunderstandingoftheSoStypescanbeobtaineddirectlythroughthemostpopulardefinitionofSoStypesManuscriptreceivedMarch15,2022.*Corresponding
13、author.ThisworkwassupportedbytheNationalKeyResearchandDevelop-mentProgramofChina(61873236),theNaturalScienceFoundationofZhejiang Province(LZ21F020003;LY18F030001),and the CivilAerospacePre-researchProject(D020101).Journal of Systems Engineering and ElectronicsVol.34,No.3,June 2023,pp.627 64010,11.Th
14、edefinitionprovidesatext-basedinterpreta-tionofthedegreeofSoSauthority.However,becausethedefinitionlacksaquantitativejudgmentbasis,itcanbechallenging to determine the SoS type when facing apracticalexampleofanSoS22.Therefore,arigoroustheoretical foundation with unequivocal concepts isneededtoavoidva
15、guenessandsubjectivity22.AnotherkindofunderstandingoftheSoStypescanbeobtained indirectly through the well-defined theory ofSoScharacteristicsbecausetheSoStypeisthefurtherstandardizationbasedonSoScharacteristics22.ThereisabroadagreementonSoScharacteristicsthatcanhelprecognizeorrealizeanSoS23.Subseque
16、ntly,onecanthenproposeamathematicalframeworktotranslatesomeconceptsofSoScharacteristicsintoanunambiguoustheo-reticalmodelbasedonsettheory,aimingtorigorouslydefine the SoS characteristics 2426.However,theexistingdefinitionsofSoStypesusuallyrelyheavilyonthetext-baseddescriptionwithouttakingfulladvantageofthetheoreticalmodelsofSoScharacteristics.Whatismissing is a further explanation of the relationshipbetweenSoScharacteristicsandSoStypes;thisconnotesthatmoresignificanteffortmayberequiredtoexploret
