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ImplicationsofComplexityResearchforCommandandControlM.I.BellFACT,29July2009 DisclaimersMostoftheseideasarenotoriginal;IwillnotacknowledgemysourcesIamresponsibleforanyerrors;feelfreetopointthemoutComplexitycanbecomplicated,evencomplexIgetnothingfromtheadmissioncharge;norefundswillbegiven2 BewareofHumptyDumpty“WhenIuseaword,”HumptyDumptysaid,inratherascornfultone,“itmeansjustwhatIchooseittomean–neithermorenorless.”“Thequestionis,”saidAlice,“whetheryoucanmakewordsmeansomanydifferentthings.”“Thequestionis,”saidHumptyDumpty,“whichistobemaster–that'sall.”CareisrequiredwhenusingeverydaywordsforspecializedpurposesThecommunityofinterestneedsclear,commondefinitionThegeneralpublicneedswarningstoavoidconfusion3 OutlineMotivationSometrivialquestions(notanswers)IntuitivecomplexityQuantifyingcomplexityFormalcomplexity:dynamicandarchitecturalDesignandcontrolofcomplexsystemsComplexityandC24 MotivationComplexityasabuzzword“Sixdegreesofseparation,”“butterflyeffect,”etc.haveenteredpopularcultureDozensofuniversitygroups,programs,seminars,andprojectsPioneers(e.g.,SantaFeInstitute)consideringmovingonComplexityasametaphor98of144papersinthe14thICCRTScontaintheword“complexity”ComplexityasamindsetAwarenessofchaos,“fattails,”“tippingpoints,”self-organizationComplexityasatoolboxFractalgeometry,nonlineardynamics,agent-basedsimulationComplexityasaparadigm“acceptedexamplesofactualscientificpractice…[that]providemodelsfromwhichspringparticularcoherenttraditionsofscientificresearch”–T.S.Kuhn,TheStructureofScientificRevolutions,19625 WhatisComplexity?Manyentities,manyinteractions,collectivebehaviorQualityorquantity?Definitionorcharacteristics?Emergence,self-organization,self-similarity,chaos,etc.Computationalcomplexity(ofaproblem)Resources(typicallytime)requiredtoobtainasolutionAlgorithmicinformationcontent(ofastring)LengthoftheshortestprogramthatwilloutputthestringStructuralcomplexitySelf-similarity,fractalgeometryDynamiccomplexityChaos,sensitivitytoinitialconditions,phasetransformations6 WhyareThingsComplex?ByselectionorbydesignSelectionNaturalorartificial(oftennot“survivalofthefittest”but“thesurvivorsarethefittest”)Preferentialgrowth(“therichgetricher”)DesignNonlinearityFeedbackcontrolOptimization7 WhyDoWeCare?Emergentbehavior(self-organization)Requisitevariety(control)Causality(prediction)Stability/instability(cascadingfailure)Unintendedconsequences8 IntuitiveComplexityDisorganizedcomplexity“aprobleminwhichthenumberofvariablesisverylarge,andoneinwhicheachofthemanyvariableshasabehaviorwhichisindividuallyerratic,orperhapstotallyunknown.However,…thesystemasawholepossessescertainorderlyandanalyzableaverageproperties”Organizedcomplexity“problemswhichinvolvedealingsimultaneouslywithasizablenumberoffactorswhichareinterrelatedintoanorganicwhole”–W.Weaver,AmericanScientist(1948)9 Complexityvs.OrderPHYSICSPressureTemperaturePhaseStatisticalAnalysisOrganized/DifferentiatedEntitiesSimpleEntitiesSystemsAnalysisECONOMICSGDPGrowthrate10 ‘‘Longrangedetailedweatherpredictionisthereforeimpossible,…theaccuracyofthispredictionissubjecttotheconditionthattheflightofagrasshopperinMontanamayturnastormasidefromPhiladelphiatoNewYork!’’–W.S.Franklin(1898)ButterflyEffect11 ArgumentforQuantification“Whenyoucanmeasurewhatyouarespeakingabout,andexpressitinnumbers,youknowsomethingaboutit;butwhenyoucannotmeasureit,whenyoucannotexpressitinnumbers,yourknowledgeisofameagerandunsatisfactorykind…”–WilliamThompson(LordKelvin),1824-1907Ifwecanquantifycomplexity,wecanDeterminewhetheronesystemismoreorlesscomplexthananotherDeterminewhetheracontrol(orC2)systemisoftheappropriatecomplexityforagivensituationTakeappropriatestepstocontrolcomplexity;e.g.,ReducethecomplexityofourenvironmentIncreasethecomplexityofanadversary’senvironment12 AlgorithmicInformationContentLengthoftheshortestpossibledescriptionofasystem(madeformalusingTuringmachineconcept)Pros:ConsistentwiththeideathatagoodtheorysimplifiesthedescriptionofphenomenaCons:Complexitymayseemtobeapropertyofourunderstandingofasystem,notofthesystemitselfThelengthofdescriptionmaydependonthevocabularyavailableRelativecomplexityoftwosystemsdependsonthedetailsoftheTuringmachineusedItisimpossibletoshowthatadescriptionistheshortestpossibleRandomsystemsaremaximallycomplex(counter-intuitive)13 ComputationalComplexityThenumberofoperations(typicallymultiplications)neededtosolveaproblemPros:Acomplexproblemtakeslonger(ormoreresources)tosolvethanasimpleoneThedifficultyofacomplexproblemgrowsrapidlywithitssizen:Problemsthatcanbesolvedintimeproportionaltonkare“polynomialtime”problemsProblemsthatcanbesolvedintimeproportionaltoenorn!are“exponentialtime”problemsCons:Thereisnoalgorithmfordetermininghowhardaproblemis!14 FormalComplexityDynamic(process)CorrespondsroughlytocomputationalcomplexityOriginatedinnon-lineardynamicsArchitectural(structural)CorrespondsroughlytoalgorithmicinformationcontentOriginatedincommunicationtheory15 MandelbrotSetAcomplexnumbercisamemberofthesetifstartingwithz0=0,zn+1=zn2+cisboundedB.Mandelbrot,ca.197816 EscapeProblemsMandelbrotsetAcomplexnumbercisamemberofthesetifstartingwithz0=0,zn+1=zn2+cisboundedInotherwords,cisnotamemberifzn+1escapesSinaibilliardY.Sanai,ca.1963MadeintoanescapeproblembyBleheretal.(1988)17 SinaiBilliardx00x105x10618 PredictionHorizonDiscontinuityinboundaryconditions(aswellasnon-linearity)cancausedivergenttrajectoriesSimilarinitialconditionsproducesimilartrajectoriesforalimitedtime19 DifferentialGamesModelingconflictinadynamicalsystem(e.g.,pursuit-evasion)Eachplayer(twoormore)hasastate-dependentutilityfunctionthatheseekstomaximizeEachplayerhasasetofcontrolvariablesthatinfluencethestateofthesystemWhatarethebeststrategies?Whatarethepossibleoutcomes?Example:homicidalchauffeurproblem(R.Isaacs,1951)The“pedestrian”isslowbuthighlymaneuverableThe“vehicle”ismuchfasterbutfarlessmaneuverableUnderwhatinitialconditions(ifany)canthepedestrianavoidbeingrunoverindefinitely?Somegames(complexones?)generatestate-spacestructureswithfractalgeometry20 ControlSystemsControllerSystemSensor+–ModelGoalControllerSystemOpenLoopClosedLoop21 Aircraft(N=6,Nc=3,4)andautomobiles(N=3,Nc=2)arenon-holonomicNostablecontrolsettingsarepossible;noteverypathcanbefollowedEverypossiblepathcanbeapproximatedControlTheoryDegreesoffreedom(sixforanaircraft)(x,y,z)=coordinatesofcenterofmass(,,)=yaw,pitch,rollHolonomicityNdegreesoffreedomNccontrollabledegreesoffreedomSystemisHolonomicifNc=NNon-holonomicifNc
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《implications of complexity research for command and cont:复杂性研究的指挥和控制的影响》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
ImplicationsofComplexityResearchforCommandandControlM.I.BellFACT,29July2009 DisclaimersMostoftheseideasarenotoriginal;IwillnotacknowledgemysourcesIamresponsibleforanyerrors;feelfreetopointthemoutComplexitycanbecomplicated,evencomplexIgetnothingfromtheadmissioncharge;norefundswillbegiven2 BewareofHumptyDumpty“WhenIuseaword,”HumptyDumptysaid,inratherascornfultone,“itmeansjustwhatIchooseittomean–neithermorenorless.”“Thequestionis,”saidAlice,“whetheryoucanmakewordsmeansomanydifferentthings.”“Thequestionis,”saidHumptyDumpty,“whichistobemaster–that'sall.”CareisrequiredwhenusingeverydaywordsforspecializedpurposesThecommunityofinterestneedsclear,commondefinitionThegeneralpublicneedswarningstoavoidconfusion3 OutlineMotivationSometrivialquestions(notanswers)IntuitivecomplexityQuantifyingcomplexityFormalcomplexity:dynamicandarchitecturalDesignandcontrolofcomplexsystemsComplexityandC24 MotivationComplexityasabuzzword“Sixdegreesofseparation,”“butterflyeffect,”etc.haveenteredpopularcultureDozensofuniversitygroups,programs,seminars,andprojectsPioneers(e.g.,SantaFeInstitute)consideringmovingonComplexityasametaphor98of144papersinthe14thICCRTScontaintheword“complexity”ComplexityasamindsetAwarenessofchaos,“fattails,”“tippingpoints,”self-organizationComplexityasatoolboxFractalgeometry,nonlineardynamics,agent-basedsimulationComplexityasaparadigm“acceptedexamplesofactualscientificpractice…[that]providemodelsfromwhichspringparticularcoherenttraditionsofscientificresearch”–T.S.Kuhn,TheStructureofScientificRevolutions,19625 WhatisComplexity?Manyentities,manyinteractions,collectivebehaviorQualityorquantity?Definitionorcharacteristics?Emergence,self-organization,self-similarity,chaos,etc.Computationalcomplexity(ofaproblem)Resources(typicallytime)requiredtoobtainasolutionAlgorithmicinformationcontent(ofastring)LengthoftheshortestprogramthatwilloutputthestringStructuralcomplexitySelf-similarity,fractalgeometryDynamiccomplexityChaos,sensitivitytoinitialconditions,phasetransformations6 WhyareThingsComplex?ByselectionorbydesignSelectionNaturalorartificial(oftennot“survivalofthefittest”but“thesurvivorsarethefittest”)Preferentialgrowth(“therichgetricher”)DesignNonlinearityFeedbackcontrolOptimization7 WhyDoWeCare?Emergentbehavior(self-organization)Requisitevariety(control)Causality(prediction)Stability/instability(cascadingfailure)Unintendedconsequences8 IntuitiveComplexityDisorganizedcomplexity“aprobleminwhichthenumberofvariablesisverylarge,andoneinwhicheachofthemanyvariableshasabehaviorwhichisindividuallyerratic,orperhapstotallyunknown.However,…thesystemasawholepossessescertainorderlyandanalyzableaverageproperties”Organizedcomplexity“problemswhichinvolvedealingsimultaneouslywithasizablenumberoffactorswhichareinterrelatedintoanorganicwhole”–W.Weaver,AmericanScientist(1948)9 Complexityvs.OrderPHYSICSPressureTemperaturePhaseStatisticalAnalysisOrganized/DifferentiatedEntitiesSimpleEntitiesSystemsAnalysisECONOMICSGDPGrowthrate10 ‘‘Longrangedetailedweatherpredictionisthereforeimpossible,…theaccuracyofthispredictionissubjecttotheconditionthattheflightofagrasshopperinMontanamayturnastormasidefromPhiladelphiatoNewYork!’’–W.S.Franklin(1898)ButterflyEffect11 ArgumentforQuantification“Whenyoucanmeasurewhatyouarespeakingabout,andexpressitinnumbers,youknowsomethingaboutit;butwhenyoucannotmeasureit,whenyoucannotexpressitinnumbers,yourknowledgeisofameagerandunsatisfactorykind…”–WilliamThompson(LordKelvin),1824-1907Ifwecanquantifycomplexity,wecanDeterminewhetheronesystemismoreorlesscomplexthananotherDeterminewhetheracontrol(orC2)systemisoftheappropriatecomplexityforagivensituationTakeappropriatestepstocontrolcomplexity;e.g.,ReducethecomplexityofourenvironmentIncreasethecomplexityofanadversary’senvironment12 AlgorithmicInformationContentLengthoftheshortestpossibledescriptionofasystem(madeformalusingTuringmachineconcept)Pros:ConsistentwiththeideathatagoodtheorysimplifiesthedescriptionofphenomenaCons:Complexitymayseemtobeapropertyofourunderstandingofasystem,notofthesystemitselfThelengthofdescriptionmaydependonthevocabularyavailableRelativecomplexityoftwosystemsdependsonthedetailsoftheTuringmachineusedItisimpossibletoshowthatadescriptionistheshortestpossibleRandomsystemsaremaximallycomplex(counter-intuitive)13 ComputationalComplexityThenumberofoperations(typicallymultiplications)neededtosolveaproblemPros:Acomplexproblemtakeslonger(ormoreresources)tosolvethanasimpleoneThedifficultyofacomplexproblemgrowsrapidlywithitssizen:Problemsthatcanbesolvedintimeproportionaltonkare“polynomialtime”problemsProblemsthatcanbesolvedintimeproportionaltoenorn!are“exponentialtime”problemsCons:Thereisnoalgorithmfordetermininghowhardaproblemis!14 FormalComplexityDynamic(process)CorrespondsroughlytocomputationalcomplexityOriginatedinnon-lineardynamicsArchitectural(structural)CorrespondsroughlytoalgorithmicinformationcontentOriginatedincommunicationtheory15 MandelbrotSetAcomplexnumbercisamemberofthesetifstartingwithz0=0,zn+1=zn2+cisboundedB.Mandelbrot,ca.197816 EscapeProblemsMandelbrotsetAcomplexnumbercisamemberofthesetifstartingwithz0=0,zn+1=zn2+cisboundedInotherwords,cisnotamemberifzn+1escapesSinaibilliardY.Sanai,ca.1963MadeintoanescapeproblembyBleheretal.(1988)17 SinaiBilliardx00x105x10618 PredictionHorizonDiscontinuityinboundaryconditions(aswellasnon-linearity)cancausedivergenttrajectoriesSimilarinitialconditionsproducesimilartrajectoriesforalimitedtime19 DifferentialGamesModelingconflictinadynamicalsystem(e.g.,pursuit-evasion)Eachplayer(twoormore)hasastate-dependentutilityfunctionthatheseekstomaximizeEachplayerhasasetofcontrolvariablesthatinfluencethestateofthesystemWhatarethebeststrategies?Whatarethepossibleoutcomes?Example:homicidalchauffeurproblem(R.Isaacs,1951)The“pedestrian”isslowbuthighlymaneuverableThe“vehicle”ismuchfasterbutfarlessmaneuverableUnderwhatinitialconditions(ifany)canthepedestrianavoidbeingrunoverindefinitely?Somegames(complexones?)generatestate-spacestructureswithfractalgeometry20 ControlSystemsControllerSystemSensor+–ModelGoalControllerSystemOpenLoopClosedLoop21 Aircraft(N=6,Nc=3,4)andautomobiles(N=3,Nc=2)arenon-holonomicNostablecontrolsettingsarepossible;noteverypathcanbefollowedEverypossiblepathcanbeapproximatedControlTheoryDegreesoffreedom(sixforanaircraft)(x,y,z)=coordinatesofcenterofmass(,,)=yaw,pitch,rollHolonomicityNdegreesoffreedomNccontrollabledegreesoffreedomSystemisHolonomicifNc=NNon-holonomicifNc
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