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1、ProceedingsoftheAmericanControlConferenceAnchorage,AKMay8-10,2002NonlinearObserverDesignviaConvexOptimizationAdamHowellJ.KarlHedrickMechanicalEngineeringDepartmentMechanicalEngineeringDepartmentUniversityofCalifornia,Berkeley94720UniversityofCalifornia,Berkeley94720ahowell@vehicle.me.
2、berkeley.edukhedrick@vehicle.me.berkeley.eduAbstractandnumericallytractablebecausetheycaneasilybeformulatedasaconvexoptimizationproblem[2].Thispaperpresentsanonlinearobserverdesigntech-niquebasedonLyapunov’ssecondmethodwhichpro-Despitethislonghistoryofinterestinthecontrolofvidesanobse
3、rvergainmatrixthatstabilizestheerrorLur’esystems,verylittleofthisworkhasbeenapplieddynamicsforaclassofnonlinearsystems.Itwillalsototheobserverdesignofsuchsystems.Thispaperwillbeshownhowtheobservergainmatrixcanbeopti-developanonlinearobserverdesigntechniquebasedmallychosen,viaconvexopt
4、imization,withrespecttoonLyapunov’ssecondmethodwhichprovidesanob-threedifferentcosts;specifically,themaximumsingu-servergainmatrixthatstabilizestheerrordynamicslarvalueofthegainmatrix,thedecayrateoftheerrorforaclassofnonlinearsystems.Itwillalsobeshowndynamics,andthe%,normbetweendistur
5、bancesandhowtheobservergainmatrixcanbeoptimallychosen,theestimationerrors.Furthermore,thepaperwilldis-viaconvexoptimization,withrespecttothreedifferentcusshowthesedifferentoptimizationcriteriacanbecosts;specifically,themaximumsingularvalueofthecombinedtoprovideParetooptimalobservergai
6、nma-gainmatrix,thedecayrateoftheerrordynamics,andtrices.Simulationresultsforarepresentativeproblemthe%,normbetweendisturbancesandtheestima-willalsobegiven.tionerrors.Furthermore,thepaperwilldiscusshowtheseoptimizationcriteriacmbecombinedtoprovideParetooptimalobservergainmatrices.1Intr
7、oductionTheremainderofthepaperisdividedasfollows;Sec-tion2willdiscusstheclassofproblemsthatwillbeThedesignofnonlinearobservershasachievedconsid-considered,whileSection2willpresentthederivationerableattentionrecently,andasaresultawidevarietyofsufficientconditionsfortheexistenceofanobse
8、rvero
