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1、AConvexifyingAlgorithmfortheDesignofStructuredLinearControllers1M.C.deOliveira,J.F.CaminoandR.E.Skelton2AbstractIntheLMIframework,alinearcontrolsynthesisproblemisusuallysolvedwiththehelpofauxiliaryparametriza-Thispaperaddressesthedesignoflinearcontrollerswithtions[1].Thatis,thecontrollerparam
2、etersarenotavailablespecialstructureimposedonthegainmatrix.Thisproblemforoptimization,beingobtainedviasomenonlinearone-to-iscalledaSLC(StructuredLinearControl)problem.Theonetransformationoftheoptimizationvariables.CallingHsSLCproblemincludesfixedorderoutputfeedbackcontrol,thetransferfunction
3、fromagiveninputtoagivenout-decentralizedcontrol,jointplantandcontroldesign,andput,onecan,roughlyspeaking,solveseverallinearcontrolmanyotherlinearcontrolproblems.Atheoreticalframe-problemintheformworkthatallowsonetopursuethesolutionofSLCproblemsminfHsisprovided.Althoughtheobtainedconditionsa
4、renoncon-K(1)vex,itisshownthatsolvingaSLCprobleminvolvingstan-wherefissomeappropriatelydefinedcostfunction.No-dardcontrolobjectivessuchasstability,boundsontheH2orticethatthecontrollergainKinproblem(1)isanuncon-H¥norms,andrealpositivenessisnotharderthansolvingastrainedvariable.Thestruct
5、ureofthecontrollerisimposedstandardunstructuredstaticoutputfeedbackproblem.bythepropertiesoftheproblemsolution.AsaconsequenceAconvexifyingalgorithmthatmightbeusedtosolvetheofthisfact,fundamentalproblemssuchasthedesignofSLCproblemisalsodeveloped.Ateachiterationacertaincontrollerswitharbitraryo
6、rder[2]orwithparticularstruc-functionisaddedtotheconstraintsinordertomakethemtures,suchasdecentralization[3],remainunsolved.Inotherconvex.Atconvergence,theartificiallyintroducedconvex-words,linearcontrolproblemsoftheformifyingfunctionsreducetozero,guaranteeingthefeasibilityminfHsoftheorigina
7、lproblem.Localoptimalitycanbeguaranteed.K(2)!YSomeexamplesillustratehowtheSLCframeworkandthewherethecontrollerKissubjecttoconstraintsarehardtoconvexifyingalgorithmcanimprovethesolutionsofcontrolhandle.EvenconvexityofYprovideslittleornohe