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简介：Thispaperaddressesanonlinearfeedbackcontrolproblemforthechaoticarchmicro-electro-mechanicalsystemwithunknownparameters,immeasurablestatesandpartialstate-constraintsubjectedtothedistributedelectrostaticactuation.Toreflectinherentpropertiesanddesigncontroller,thephasediagrams,bifurcationdiagramandPoincaresectionarepresentedtoinvestigatethenonlineardynamics.TheauthorsemployasymmetricbarrierLyapunovfunctiontopreventviolationofconstraintwhenthearchmicro-electro-mechanicalsystemfacessomelimits.AnRBFneuralnetworksystemintegratingwithanupdatelawisadoptedtoestimateunknownfunctionwitharbitrarilysmallerror.Toeliminatechaoticoscillation,aneuro-adaptivebacksteppingcontrolschemefusedwithanextendedstatetrackingdifferentiatorandanobserverisconstructedtolowerrequirementsonmeasuredstatesandprecisesystemmodel.Besides,introducinganextendedstatetrackingdifferentiatoravoidsrepeatedderivativeforthevirtualcontrolsignalassociatedwithconventionalbackstepping.Finally,simulationresultsarepresentedtoillustratefeasibilityoftheproposedscheme.

简介：Fromamathematicalmodelofonekindcomplicatedfinancialsystem,correspondinglocaltopologicalstructuresofsuchkindsystemonconditionofcertainparametercombination,unstableequilibriumpointofthesystem,conditionsonwhichHopfbifurcationiscreatedandstabilityofthelimitcirclecorrespondingtotheHopfbifurcationaswellasconditiononwhichthelimitcircleisstablehavebeenstudied.FromrelationshipbetweeneachparameterandtheHopfbifurcationallthewaytoroutewhichleadstochaosetchavebeenstudied.Followingtheabove,conditionsonwhichcomplicatedbehaviorscreatedlocallyinsuchkindsystemhasbeenanalyzed.Byapplyingfractaldimension,Lyapunovindex,theintrinsiccomplexityofthesystemonsuchconditionhasbeenstudied,andresultofthenumericalsimulationprovesthetheoryofthispapercorrect.

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