State and parameter estimation for nonlinear systems A Takagi-Sugeno approach

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1、2013AmericanControlConference(ACC)Washington,DC,USA,June17-19,2013StateandParameterEstimationforNonlinearSystems:aTakagi-SugenoApproachSouadBezzaoucha,BenoıtMarx,DidierMaquin,Jose´RagotAbstract—Themaincontributionofthispaperistoproposemeasurable(asthesyst

2、emoutput),known(asthesystemasystematicapproachtoobserverdesignforTakagi-Sugenoinput)orunmeasurable(asthesystemstate).Theweighting(T-S)time-varyingsystems.Theproposedprocedureisbasedfunctionsµi(ξ(t))ofthersubmodelssatisfytheconvexsumonthesectornonlinearity

3、approachusingtheconvexpolytopicpropertytransformation.Theexactwritingofthetime-varyingnonlinearsystemasaT-Smodelallowstoprovideastateandparameterrestimation.∑µi(ξ(t))=1(2)IndexTerms—Time-varyingnonlinearsystems,Takagi-i=1Sugenomodels,sectornonlinearity

4、approach,convexpolytopic0≤µi(ξ(t))≤1,i=1,...,rtransformation,stateandparameterobserver,linearmatrixThisrepresentationisveryinterestinginthesensethatinequality.itsimplifiesthemathematicalmanipulationcomparedtoI.INTRODUCTIONtheoriginalnonlinearmodel.Itallows

5、toextendtheuseofsometoolsdevelopedinthelinearframeworktotheTheobserverdesignfornonlinearsystemscanbeviewednonlinearsystems,forthestabilitystudy,thecontroldesignastheheartofsystemcontrolandmodel-baseddiagnosis[5],andobserversynthesis.[2].Unfortunately,thei

6、ntroductionoftime-varyingparam-Asystematicproceduretotransformanonlinearsystembyetersinthesystemmodels,neededtoaccuratelyrepresentrewritingitintoaT-Sform,withoutanylossofinformationthesystembehaviour,leadstomorechallengingproblemsinisknownasthesectornonli

7、nearitytransformation(SNT)estimation.[13],[9].ThistransformationadvantageistobeanalyticalInthepresentwork,afocusismadeonthetime-varyingandsystematic.Basedonthenonlinearequationsoftheparametersystems,wheretheparametervariationsareinac-originalmodel,aquasi-

8、LinearParameterVarying(quasi-cessible(nonmeasurable)andmaybeusedasmodelfaultsLPV)iswritten.Thelocalmodelsofthisformarestate(actingasdisturbancesor/anduncertainties).Inthiscase,aandcontrolinputaffine,however,thisrepre