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1、2IEEETRANSACTIONSONAUTOMATICCONTROL,VOL.56,NO.1,JANUARY2011DisturbanceDecouplingofBooleanControlNetworksDaizhanCheng,Fellow,IEEEAbstract—Disturbancedecouplingproblem(DDP)ofBoolean[9],usingtheinput-stateanalysis,thestructureofattractorsofcontrolnetworksisconsidered.
2、Usingsemi-tensorproductofma-aBooleannetworkisinvestigated,andsocalled“rollinggears”tricesandthematrixexpressionoflogicalfunctions,aworkingstructureisproposed,whichgivesanexplanationwhy“tinyprocedureisproposedtosolvetheproblem.Thisprocedurecon-attractors”candecideth
3、e“vast,vastorder”asdescribedin[10].sistsoftwokeydesignsteps.First,howtoconvertasystemintoanoutput-friendlycoordinateframe.Analgorithmisprovidedtocal-ThecontrollabilityandobservabilityofBooleancontrolsys-culatetheoutput-friendlysubspaces.Secondly,itwasshownhowtemsar
4、ediscussedin[11].Thecanonicalformsandrealizationtofindpropercontrollerstosolvetheproblemifitissolvable.AproblemofBooleancontrolnetworksareinvestigatedin[12].statevariableseparationformisintroducedtoguidethedesignofThisseriesofworksshowedthatthesemi-tensorproductisac
5、ontrollers.Basedonthedesigntechnique,necessaryandsufficientpowerfultoolinanalyzingthestructureofBooleannetworksconditionsareobtainedforthesolvabilityofDDP.andthesynthesisofBooleancontrolnetworks.IndexTerms—Booleancontrolnetwork,canalyzingBooleanTogiveabriefintroduct
6、iontothisnewframework,wefirstmapping,coordinatetransformation,disturbancedecoupling,output-friendlysubspace.introducesomenotations:•.I.INTRODUCTION•,wheremeans“true”andmeans“false”.Alogicalvariablewilltakevaluefrom,whichisexpressedas.HEBooleannetwork,introducedfirstb
7、yKauffman[1],•:the-thcolumnoftheidentitymatrix.Thasbeenprovedtobequiteusefulinmodelingandquanti-•,.tativedescriptionofcellularregulators[2]–[4].Kauffmanmen-•AmatrixiscalledaBooleanmatrix,ifallitstionedthat[5]“SwitchingBooleannetworksareofcentralim-entriesareeither0
8、or1.ThesetofBooleanmatricesportancetotheconstructionofastatisticalmechanicsoveren-isdenotedby.semblesofsystemsandtoanadequatetheoryofcomplexbut•A
