本科畢業(yè)設(shè)計（論文）外文翻譯專業(yè)電氣及其自動化所在學院電子信息工程學院二零一二年六月ITERATIVESLIDINGMODECONTROLABSTRACTITERATIVELEARNINGCONTROLILCMETHODSAREDESCRIBEDANDAPPLIEDEVERINCREASINGLYASPOWERFULTOOLSTOCONTROLDYNAMICSNOWADAYSILCSMETHODSINMOSTSTUDIESAREDESCRIBEDASBASEDONREPETITIVEPROCESSFROMTHEBEGINNINGTOTHEENDOFPROCESSORASAKINDOFREPETITIVECONTROLOURNEWLYDESIGNEDCONTROLLERSBASEDONAPARTICULARCASEOFITERATIVELEARNINGCONTROLRADICALLYDIFFERFROMCONVENTIONALMETHODSINATTEMPTINGTOSTABILIZEACLASSOFNONLINEARSYSTEMSINTHISPAPERTWOKINDSOFILCMETHODAREINTRODUCEDINTWOSEPARATESECTIONSINTHEFIRST,OURNEWLYDESIGNEDMETHODSATISFIESTHECONDITIONOFALYAPUNOVSTABILITYTHEOREMINACLASSOFNONLINEARSYSTEMSINWHICHTHEIRSTRUCTURESHAVETHELIPSCHITZPROPERTYINTHESECOND,BYFREEZINGTHETIMEANDMOVINGTOANEWVIRTUALAXIS,CALLEDTHEINDEXAXIS,THISNEWLYDESIGNEDMETHODTRIESTOFINDTHEBESTVALUEFORCONTROLATTHISTIMESTEPANDCANBEUSEDINTWOMODES,ONLINEANDOFFLINEINBOTHMETHODS,BYSATISFYINGTHECONVERGENCECONDITIONOFOURDESIGNEDILC,CLOSEDLOOPSTABILITYISOBTAINEDAUTOMATICALLYKEYWORDSITERATIVELEARNINGCONTROL,NONLINEARSYSTEMS,LYAPUNOVSTABILITYTHEOREMSECTIONAANEWAPPROACHTOSTABILIZEACLASSOFNONLINEARSYSTEMSBYILCMETHODINRECENTDECADES,RESEARCHERSHAVEBEENFOCUSINGEFFORTSONLEARNINGCONTROLSYSTEMS,SOTHATTHISKINDOFCONTROLTECHNIQUEISABLETOIMPROVESYSTEMPERFORMANCEEFFICIENTLYMANYSCIENTISTSWORKINGONITERATIVELEARNINGCONTROLILCHAVEPRESENTEDDIFFERENTLEARNINGCONTROLSCHEMESAMONGTHESE,FORTRACKINGCONTROL,ISTHEITERATIVELEARNINGCONTROLWHICHWASORIGINALLYINTRODUCEDBYARIMOTOIN19841,2THEMAINPURPOSEOFILCISTOFINDACONTROLINPUTITERATIVELY,RESULTINGINTHEPLANTSABILITYTOTRACKTHEGIVENREFERENCESIGNALWITHANOUTPUTTRAJECTORYOVERAFINITETIMEINTERVALCOMMONILCMETHODSUSETHEREPETITIVENATUREOFTHEPROCESSTOIMPROVETHETRACKINGPERFORMANCEPROGRESSIVELYBUTFROMANEWVIEWPOINTONILC,WHICHISREPRESENTEDINTHISPAPER,STABILITYOFACLASSOFNONLINEARSYSTEMSWOULDBEOBTAINEDA1INTRODUCTIONINRECENTDECADES,RESEARCHERSHAVEBEENFOCUSINGEFFORTSONLEARNINGCONTROLSYSTEMS,SOTHATTHISKINDOFCONTROLTECHNIQUEISABLETOIMPROVESYSTEMPERFORMANCEEFFICIENTLYMANYSCIENTISTSWORKINGONITERATIVELEARNINGCONTROLILCHAVEPRESENTEDDIFFERENTLEARNINGCONTROLSCHEMESAMONGTHESE,FORTRACKINGCONTROL,ISTHEITERATIVELEARNINGCONTROLWHICHWASORIGINALLYINTRODUCEDBYARIMOTOIN19841,2THEMAINPURPOSEOFILCISTOFINDACONTROLINPUTITERATIVELY,RESULTINGINTHEPLANTSABILITYTOTRACKTHEGIVENREFERENCESIGNALWITHANOUTPUTTRAJECTORYOVERAFINITETIMEINTERVALCOMMONILCMETHODSUSETHEREPETITIVENATUREOFTHEPROCESSTOIMPROVETHETRACKINGPERFORMANCEPROGRESSIVELYBUTFROMANEWVIEWPOINTONILC,WHICHISREPRESENTEDINTHISPAPER,STABILITYOFACLASSOFNONLINEARSYSTEMSWOULDBEOBTAINEDINSECTIONA2,THEPROBLEMFORMULATIONISPRESENTEDSECTIONA3PRESENTSOURCONTROLLERDESIGNEDMETHODSECTIONA4DISCUSSESOURRESULTSBYSHOWINGAPPLICATIONOFOURALGORITHMTOSOMEDYNAMICSA2PROBLEMFORMULATIONCONSIDERTHESYSTEM1WHEREAREPIECEWISECONTINUOUSINT,ANDFISLOCALLYLIPSCHITZINXOND0,DISAMRNRDOMAINTHATCONTAINSTHEORIGINX0SUPPOSINGTHESYSTEM1ISPERTURBEDASBELOW（2）THEPERTURBATIONCOULDRESULTFROMMODELING,AGING,ORUNCERTAINTIESANDDISTURBANCESWHICHEXISTINANYREALISTICPROBLEMINATYPICALSITUATION,THOUGHTHEPERTURBATIONISNOTKNOWN,SOMEINFORMATIONSUCHASANUPPERBOUNDISAVAILABLEHERETHEPERTURBATIONISREPRESENTEDASANADDITIVETERMONRIGHTHANDSIDEOFTHESTATEEQUATIONUNCERTAINTIESWHICHDONTCHANGETHESYSTEMORDERCANALWAYSBEREPRESENTEDINTHISFORMINGENERALIFAPERTURBATIONISCONSIDEREDASHX,T,ITCANBECLASSIFIEDINTWOTYPESASBELOWHX,T0ISAVANISHINGPERTURBATION,ANDHX,T0ISCALLEDANONVANISHINGPERTURBATIONINTHISPAPER,VANISHINGPERTURBATIONSHAVEBEENINVESTIGATEDFORTHEFUNCTIONGWHEREASTHEPERTURBATIONOFFISCONSIDEREDTOBELIPSCHITZITISNECESSARYTOFULFILLTHESEFOURASSUMPTIONS1THEPERTURBATIONOFGISVANISHINGG0,T0,ANDITSUPPERBOUNDISKNOWNASGX,T2FISPIECEWISECONTINUOUSINTIME,ANDLOCALLYLIPSCHITZIND0,D,IEFX,TNRF0,TMX3F0,T0X0ISANEQUILIBRIUMPOINTOFTHEUNPERTURBEDSYSTEM4THEPERTURBATIONOFF,FX,T,SATISFIESTHELIPSCHITZCONDITIONA3CONTROLLERDESIGNMETHODFORACLOSEDLOOPSYSTEM,THESTATESPACEEQUATIONISGIVENBY1USUALLYSTABILIZATIONOFTHECLOSEDLOOPSYSTEMCANBEPREPAREDBYASUITABLECONTROLLERUX,TASAFUNCTIONOFSTATEXANDTIMETFORSUCHASYSTEM1,BYTHETHEOREMDISCUSSEDBELOW,WECLAIMTHATASTABILIZERINTHEFORMOFAFEEDBACKCONTROLANDALYAPUNOVFUNCTIONFORSTABILIZINGTHESYSTEMAREFOUNDTHEOREMCONSIDERTHECLOSEDLOOPSYSTEM3WITHTHEFOLLOWINGCONTROLLERUKX3WHEREKISAMATRIXWHICHGOVERNEDBYTHEFOLLOWINGLAWMIGX,TK4DQWHEREMISBOUNDOFTHELIPSCHITZCONDITION,IISAUNITMATRIXWITHPROPERDIMENSION,ANDISDQADESIREDNEGATIVEDEFINITEMATRIXWHICHISSELECTEDBYTHEDESIGNERBASEDONTHERATEOFDESCENDINGOFTHELYAPUNOVCRITERIONTHEN3WILLBEASYMPTOTICALLYSTABLEAROUNDTHEORIGINPROOFBYDEFININGTHELYAPUNOVFUNCTION,ASBELOWANDFOLLOWINGTHEPROOFPROCEDURE,ASUITABLECONTROLLERWILLBEDERIVEDASFOLLOWBYUSINGTHESCHWARTZINEQUALITYWEHAVEANDBYIMPLEMENTINGTHELIPSCHITZCONDITIONTHISCHANGESTONOWBYSELECTINGTHECONTROLLERASUKX,THEFOLLOWINGRELATIONISACHIEVEDTHEREFORETHEDESIREDNEGATIVEDEFINITEMATRIXISDQSINCETHEKMATRIXCANBEOBTAINEDFROMTHEFOLLOWINGCASESASBELOWCASE1GISANINVERTIBLEMATRIXINTHISCASEKISOBTAINEDSIMPLYBYTHEFOLLOWINGRELATIONTESTA6CASE2GISAPSEUDOINVERTIBLEMATRIXHEREKCANBEEXPRESSEDBYTESTA7OURALGORITHMISALSORELIABLEFORSYSTEMS1INWHICHTHEINPUTANDOUTPUTSNUMBESAREDIFFERENTIFGX,TISNOTINVERTIBLEORPSEUDOINVERTIBLE,THISMEANSTHATTHEINPUTSINTERACTINTHISCASE,THECONTROLLABILITYPROBLEMMAYARISEATTHISTIMETHEILCMETHODISMOREEFFECTIVECOROLLARYINTHEGENERALCASE,GHASNMDIMENSIONWHERENISTHENUMBEROFSTATESANDMISTHENUMBEROFINPUTSINTHISCASEITERATIVELEARNINGCONTROLCANBEUSEDTOFINDTHEDESIREDKMNMATRIXWHICHSATISFIESRELATION9BYTHEFOLLOWINGMETHODTESTA1WHEREIREPRESENTSTHEITERATIONINDEXANDISTHELEARNINGFACTORMATRIXANDISGIVENBYNMIEITSHOULDBECONSIDEREDTHATTHISTYPEOFCONTROLISUSEDWHENTHESYSTEMANDTHECONTROLLERHAVEDIFFERENTTIMERATESOFPROCESSING,MEANINGTHATTHEDESIREDCONTROLLERWORKSMUCHFASTERTHANTHEPROCESS,POSSIBLYBYUSINGMODERNHIGHRATESOFTWAREREMARKA1ROBUSTNESSWITHRESPECTTOPERTURBATIONSINFANDGCONSIDERFANDGPERTURBEDBYTHETERMSFANDGSUPPOSETHEPERTURBATIONOFFISVANISHING,WHICHSATISFIESTHELINEARGROWTHBOUNDWHEREISANONNEGATIVECONSTANTALSOFORTHEPERTURBATIONOFG,ITISSUPPOSEDTHATITSUPPERBOUNDISKNOWN,THEREFOREITCANBEWRITTENASWHEREISAPOSITIVENUMBER迭代滑?？刂普缃?，迭代學習控制（ILC）方法的描述和應(yīng)用日益成為強大的工具用來控制動力學。迭代學習控制方法在大多數(shù)研究方法的基礎(chǔ)上重復(fù)著從開始到結(jié)束的過程，或作為一種描述重復(fù)控制。基于特定情況下的迭代學習控制，我們新設(shè)計的控制器從根本上不同于傳統(tǒng)的方法，它是在嘗試一類非線性系統(tǒng)的穩(wěn)定。本文介紹兩種迭代學習控制方法在這兩個獨立的部分。第一，我們新的設(shè)計方法滿足在一類非線性系統(tǒng)中其結(jié)構(gòu)有李氏的李雅普諾夫穩(wěn)定性定理的條件。第二，通過凍結(jié)的時間和移動到一個新的虛擬軸（稱為指數(shù)軸），在這個新的設(shè)計方法中，試圖找到最好能控制在這個時間步長值上并可用于兩種模式下，上線和離線。這兩種方法都可以滿足我們設(shè)計的迭代學習控制的銜接條件，所以閉環(huán)穩(wěn)定自動獲得。關(guān)鍵詞迭代學習控制，非線性系統(tǒng)，李雅普諾夫穩(wěn)定性定理第一部分一種新方法穩(wěn)定的一類非線性系統(tǒng)的迭代學習控制方法11介紹近幾十年來，研究人員一直集中在學習控制系統(tǒng)的努力中，使這種控制技術(shù)能夠有效地提高系統(tǒng)性能。許多致力于迭代學習控制（ILC）工作的科學家們已經(jīng)提出了不同的學習控制方案。其中，跟蹤控制，最初是由ARIMOTO在1984年推出的一種迭代學習控制。迭代學習控制的主要目的是為了找到一個迭代控制輸入，導(dǎo)致了設(shè)備在有限的時間間隔內(nèi)跟蹤給定的輸出軌跡參考信號的能力。常見的迭代學習控制方法采用了過程中的重復(fù)性質(zhì)來逐步提高跟蹤性能。但是，從本文提到的一種新的迭代學習控制觀點來看，可以獲得這一類非線性系統(tǒng)的穩(wěn)定性。12問題制定考慮到系統(tǒng)1（2）由模型、老化或在任何現(xiàn)實中存在的不確定性或干擾都可能導(dǎo)致的擾動問題。在一個典型的情況下，雖然不知道擾動，