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1、algorithmsArticleRobustFuzzyAdaptiveSlidingModeStabilizationforFractional-OrderChaosBachirBourouba1andSamirLadaci2,3,*ID1DepartmentofElectricalEngineering,Sétif1University,Sétif19000,Algeria;bachir.bourouba@univ-setif.dz2DepartmentofElectronics,ElectrotechnicsandAutomatics(EEA),Office447,BP7
2、5A,NationalPolytechnicSchoolofConstantine,NouvellevilleAliMendjli,Constantine25100,Algeria3LaboratoryofSignalProcessing(SP-Lab),DepartmentofElectronics,UniversityofMentouriBrothersConstantine1,RoutedeAinElbey,Constantine25000,Algeria*Correspondence:samir.ladaci@enp-constantine.dzorsamir_lad
3、aci@yahoo.fr;Tel.:+213-7-77809846Received:1June2018;Accepted:5July2018;Published:7July2018Abstract:Inthispaper,anewadaptivefuzzyslidingmodecontrol(AFSMC)designstrategyisproposedforthecontrolofaspecialclassofthree-dimensionalfractionalorderchaoticsystemswithuncertaintiesande
4、xternaldisturbance.Thedesignmethodologyisdevelopedintwostages:first,anadaptiveslidingmodecontrollawisproposedfortheclassoffractionalorderchaoticsystemswithoutuncertainties,andthenafuzzylogicsystemisusedtoestimatethecontrolcompensationefforttobeaddedinthecaseofuncertaintiesonthesystem’smodel.
5、BasedontheLyapunovtheory,thestabilityanalysisofbothcontrollawsisprovidedwitheliminationofthechatteringactioninthecontrolsignal.ThedevelopedcontrolschemeissimpletoimplementandtheoverallcontrolschemeguaranteestheglobalasymptoticstabilityintheLyapunovsenseifalltheinvolvedsignalsareuniformlybou
6、nded.Inthepresentwork,simulationstudiesonfractional-orderChenchaoticsystemsarecarriedouttoshowtheefficiencyoftheproposedfractionaladaptivecontrollers.Keywords:chaoticsystems;fractional-ordersystem;slidingmodecontrol;adaptivefuzzycontrol;Lyapunovstability1.IntroductionItisundeniablethatfracti
7、onal-calculus(computationofderivativesandintegralsofanyarbitraryrealorcomplexorder)anditsapplicationsfocusedmuchinterestinthelastthreedecades[1].Thisgrowingpopularityandimportanceismainlyduetoitsdemonstratedapplicationsinnumerousseeminglydiversefieldsofsc
