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基于有限时间的一类时滞非线性切换系统滑模控制.docx

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基于有限时间的一类时滞非线性切换系统滑模控制 Title:SlidingModeControlforaClassofTime-DelayNonlinearSwitchedSystemsunderLimitedTime Abstract: Inrecentyears,thecontrolofnonlinearswitchedsystemswithtimedelayshasgainedsignificantattentionduetoitspracticalimportanceinvariousengineeringapplications.Thispaperfocusesonthedesignofaslidingmodecontrolforaclassoftime-delaynonlinearswitchedsystemsunderlimitedtime.Theobjectiveistostabilizethesystembyensuringfinite-timeconvergencetoadesiredslidingsurfacedespitetheinfluenceoftimedelaysandsystemuncertainties.Theproposedcontrolschemeisrobustandeffectiveindealingwiththechallengesposedbytimedelaysanduncertainties. 1.Introduction: Nonlinearswitchedsystemswithtimedelayshavebeenwidelyusedtomodelcomplexdynamicalsystemsinvariousfields,includingrobotics,powersystems,chemicalprocesses,andcommunicationnetworks.Thepresenceoftimedelaysintroducesadditionalchallengesincontroldesignduetotheirinherentinstabilityandpotentialoscillations.Slidingmodecontrolhasbeenproventobeaneffectiveapproachforstabilizingnonlinearsystems.Thispaperproposesaslidingmodecontrolstrategyspecificallytailoredfortime-delaynonlinearswitchedsystemsunderlimitedtime. 2.Problemformulation: Consideraclassoftime-delaynonlinearswitchedsystemsdescribedbythefollowinggeneralform: ẋ(t)=fᵢ(x(t-τᵢ)),t≥0 wherex(t)∈ℝⁿrepresentsthesystemstateattimet,fᵢisacontinuousandboundednonlinearfunction,τᵢisthetimedelayassociatedwiththeswitchingmodei,andiholdstheswitchingindexi∈{1,2,...,N}.Theobjectiveistodesignaslidingmodecontrollerthatensuresfinite-timeconvergencetoadesiredslidingsurfacedespitetheinfluenceoftimedelaysandsystemuncertainties. 3.SlidingModeControlDesign: Theproposedslidingmodecontrolforthetime-delaynonlinearswitchedsystemsisdesignedasfollows: U(t)=-K(s)·sgn(s)+B(s)·ψ(t) whereU(t)isthecontrolinput,K(s)istheslidingmodegainmatrix,sistheslidingsurface,sgn(s)isthesignumfunction,ψ(t)isthereachinglaw,andB(s)isapositivedefinitematrixsatisfyingacertainstabilitycondition. 4.StabilityAnalysis: Thestabilityanalysisofthepro