H-鲁棒控制理论发展的十年回顾

H张显库　贾欣乐　王兴成　杨承恩(,116026)回顾了状态空间H∞鲁棒控制理论十年的发展历史。首先介绍了H∞鲁棒控制理论的概念及实质,然后将其发展过程划分为4个阶段,给出了国际著名学者的重要成果年代文献表,并归纳出H∞鲁棒控制理论的特点,简介了小增益理论、回路成形及分析的主要内容,最后讨论了H∞鲁棒控制理论尚待研究的几个问题。H∞鲁棒控制理论,小增益理论,回路成形,分析TP131H∞鲁棒控制理论的概念及实质HH(Hardy)H,F:=supRe(s)0-[F(s)]=supR-[F(j)](1)F(s)HH(MIMO)HMIMOLQG(),,,2H∞鲁棒控制理论的发展过程H,Zames[1]Doyle[2]H,H1988DoyleDGKF[2],,H,H,,H4:2.1(601980),,LQG,第14卷第4期Vol.14No.4CONTROLANDDECISION1999年7月　July19991998-07-08,1998-11-09,30,,MIMO,H2.2(19811987)1981,Zames[1]H,H,H,Youla,NehariH,(Nevanlinna-Pick),[3],HMIMO,1984,DoyleMIMOH,/,Nehari/HankelH,,,2.3(19881995)1988,DoyleDGKF[2],H,RiccatiH,()DoyleGlover[4],Khargonekar[5]H,HRiccati,,,,Windwos,H,MathWorksxMatlab;MUSYN-TOOLS;IntegratedSystemsMatrixxXmath[6],H,H,H(,,),(),,(f)Doyle[7],,,Balas1991[8],,McFarlane1992[9],H,Whittle[10],Basar[11],GreenJ[12],Dym[13],Georgiou290控　　制　　与　　决　　策1999年Gap[14],H,,,(),111981ZamesH[1]21982Doyle[7]31983Zames,FrancisNevanlinna-PickH[15]41983DoyleH[16]51984Chang,PearsonSarasonNevanlinna-PickH[17]61984Feintuch,FrancisH[18]71985Safononv,VermaHHankel[19]81985DoyleD-K[20]91986Foias,TannenbaumH[21]101987GrimbleH[22,23]111988Becker,GrimmH[24]121988Hara,SugieH[25]131988GeorgiouGapH[14]141989Doyle,GloverH[4]151989Glover,McFarlane[26]161989Gu,TsaiH[27]171990Veillette,MedanicH[28]181990GeorgiouGap[29]191991Postlethwaite-K[30]201991Balas,Doyle,Glover[8]211992SaekiH[31]221992McFarlane,Glover[9]231993Packard,Doyle[32]241994DoyleH2H[33]251995Tits,Fan[34]261996Zhou,Doyle[35]271996Skogestad,Postlethwaite[36]281997LeeH[37]1H:[38];[39];[40];[41];[42]H,H,H,291第14卷第4期张显库等:H∞鲁棒控制理论发展的十年回顾H,Doyle[43];Safonov[44];Limebeer[45];Dale[46];Guesalaga[47],H,[48,49],,H,[50,51]2.4(1996)Zhou[35],SkogestadPostlethwaite[36],H,[52],H3H∞鲁棒控制理论的特点1)MIMO,2),,,3),4)H,,4主要算法和理论的回顾H,,4.1H:Tzw,1/,1,Tzwwz,P,K,,w,,y,u,z1H2292控　　制　　与　　决　　策1999年4.22Li=KP,Lo=PK,Li,LoL(0,l),-(PK)1,-(KP)1,-(K)1(2)(h,),-(PK)1,-(KP)1,-(K)M(3)M(LoopShaping):K,L-(L)-(L),H[35]4.3(),(M)=1min{-():,det(I-M)=0}(4),I-M,(M)=0={diag[1Ir1,,sIrs,1,,F]:iC,jCmjmj},Cnn(5),1wzz=Fu(Fl(P,K),)w=Fl(Fu(P,),K)w(6)M(s)=Fl(P(s),K(s))=M11(s)M12(s)M21(s)M22(s)(7)M(s)z=Fu(M,)w=[M22+M21(I-M11)-1M12]w(8)1,M111,,P=P11P12P13P21P22P23P31P32P33(9)minKFl(P,K),=2,(10)=F3S=0,KDminKinfD,D-1HDFl(P,K)D-1(11)D-KDinfD,D-1HDFl(P,K)D-1=supinfDdd-[DFl(P,K)(j)D-1](12)D-K:D,K,H;K,D,293第14卷第4期张显库等:H∞鲁棒控制理论发展的十年回顾5H∞鲁棒控制理论尚待研究的问题1)H,,,,,Lundstrom[53]Postlethwaite[54]H,,H,H[55],,,,YangDCH[56],,2)SISO,-(L)=-(L)=L;MIMO,,,KL,P,,,,,3),minKFl(G,K)MIMO,,,4)H,1ZamesG.Feedbackandoptimalsensitivity:Modelreferencetransformations,multi-plicativeseminormsandapproxi-mateinverses.IEEETransAC,1981,26(4):301-3202DoyleJC,KGlover,PPKhargonekar.State-spacesolutionstostandardH2andHcontrolproblems.In:ACC88.Atlanta,1988.817-8233DymH.BookreviewofthecommutantliftingapproachtointerpolationproblemsbyCFoiasandAEFrazho.TheBulletinoftheAMS,1994,31:125-1404DoyleJC,KGlover,PPKhargonekar.State-spacesolutionstostandardH2andHcontrolproblems.IEEETransAC,1989,34(8):831-8475KhargonekarPP,IRPetersen,MARotea.H-optimalcontrolwithstate-feedback.IEEETransAC,1988,33(6):786-7886..:,19967DoyleJC,JEWall,GStein.Performanceandrobustnessanalysisforstructureduncertainty.In:ProcIEEECDC.Orlando,1982.671-6768BalasG,JCDoyle,KGloveretal.-analysisandsynthesistoolbox.MusynIncandtheMathworksInc.19919McFarlaneDC,KGlover.AloopshapingdesignprocedureusingHsynthesis.IEEETransAC,1992,37(6):759-76910WhittleP.Risk-sensitiveoptimalcontrol.NewYork:JWiley,199011BasarT,PBernhard.H-optimalcontrolandrelatedminimaxdesignproblems:Adynamicgameapproach.Boston:294控　　制　　与　　决　　策1999年Birkhauser,199112GreenM.HcontrollersynthesisbyJ-losslesscoprimefactorization.SIAMJControlandOptimization,1992,30(3):522-54713DymH,IGohberg.Amaximumentropyprincipleforcontractiveinterpolants.JFunctionalAnalysis,1986,65(1):83-12514GeorgiouTT.Onthecomputationofthegapmetric.SystemControlLetters,1988,11:253_25715ZamesG,BAFrancis.Feedabck,minimaxsensitivityandoptimalrobustness.IEEETransAC,1983,28(4):585_60116DoyleJC.Synthesisofrobustcontrollersandfilters.In:ProcIEEECDC.SanAntonio,1983.441-44717ChangBC,JBPearson.Optimaldisturbancereductioninlinearmultivariablesystems.IEEETransAC,1984,29(6):880_88718FeintuchA,BAFrancis.Uniformlyoptimalcontroloflineartime-varyingsystems.SystemsControlLetters,1984,5(1):67-7119SafonovMG,MVerma.L-optimizationandhankelapproximation.IEEETransAC,1985,30(2):279_28020DoyleJC.Structureduncertaintyincontrolsystemdesign.In:ProcIEEECDC85.Lauderdale,1985.260-26521FoiasC,ATannenbuam,GZames.Weightedsensitivityminimizationfordelaysystems.IEEETransAC,1986,31(6):763_76622GrimbleMJ.Hrobustcontrollerforself-tuningcontrolapplications,Part1:Controllerdesign.IntJControl,1987,46(9):1429_144423GrimbleMJ.Hrobustcontrollerforself-tuningcontrolapplications,Part2:Self-tuningandrobustness.IntJControl,1987,46(12):1819_184024BeckerN,WMGrimm.OnL2andLstabilityapproachesfortherobustcontrolofrobotmanipulators.IEEETransAC,1988,33(1):118_12225HaraS,TSugie.Independentparametrizationoftwo-degrees-of-freedomcompensatorsingeneralrobusttrackingsystems.IEEETransAC,1988,33