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1、Systems&ControlLetters14(1990)1-71North-HollandRemarksonadaptivestabilizationoffirstordernon-linearsystemsBengtM,~RTENSSONinformationofaplantistosaythatweknowthatlnstitut]'urDynamischeSysteme,UniversitiitBremen,Postfachitbelongstoacertainset~.Forexample,tosay33
2、0440,D-2800Bremen33,F.R.G.thattheplantisexactlyknownistosaythatthesetfgisasingletonset.ApieceofnecessaryaReceived19December1988prioriinformationisalimitofthesets~thatcanRevised24Julyand30September1989beadaptivelystabilized.Apieceofsufficientaprioriinformationis
3、anexistenceproof,itshowsAbstract:Adaptivestabilizationoffirstordernon-linearsys-thataset~canbeadaptivelystabilized.temsoftheform.~=f(x)+ug(x)arestudied.Forthecasewhereg(x)>0,onenecessaryandtwosufficientconditionsInthepresentpaperwewillusetheconceptofforadaptive
4、stabilizationaregiven.Forthecaseofunknownadaptivestabilizationasdefinedandusedine.g.,signofthegain,asufficientconditionisgiven.Simulation[1,6],also(forscalarplants)giveninSection2.Itresultsarepresented.isobviousthatnotallaspectsofadaptivecontrolarecoveredbytheb
5、enchmarkproblemofgettingKeywords:Adaptivestabilization;adaptivecontrol;non-linearsystems;finiteescapetime;universalcontrollers.thestatetozero,whiletheparametersconverge.Adiscussionofthesetopicsisoutsideofthescopeofthepresentwork.1.IntroductionIn[7]thefollowingc
6、onjecturewasraised:Letf9betheclassofone-dimensionallinearsystemsDuringthelastyears,considerablesuccesshasgivenby2=x+bu,whereb~O.Thenadaptivebeenmadeintheareaofadaptivestabilizationofstabilizationof~isnotpossible.(Consulttheunknownlinearsystems.Thestabilityproof
7、soforiginalpaperforthefull,slightlymoretechnical,'traditional'adaptivecontrolschemes,whichoc-formulation.)Thisconjecture,ifproventrue,curredintheendoftheseventiesandthebegin-wouldreallypinpointafundamentallimitationofningoftheeightiesallrelyonsomevariationofada
8、ptivecontrol.Ifwouldhaveshownthata'thefourassumptions'(fordetails,seee.g.certainpieceofaprioriinformation-i.e.thesign[6,5,10,8])ongivenaprioriknowledgeoftheplantofb-isabsolu
