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1、CONTROLSYSTEMS,ROBOTICS,ANDAUTOMATION–Vol.IX–RobustControl-MustafaKhammash^1ROBUSTCONTROLMustafaKhammashDepartmentofMechanicalandEnvironmentalEngineering,UniversityofCalifornia,SantaBarbara,CA93101,USAKeywords:Robustcontrol,^1control,^1optimization,Persistent
2、disturbances,^∞signals,Discrete-timesystemsContents1.Introduction2.The^1Norm3.RobustnessToSignalUncertainty:The^1NormMinimizationProblem3.1.ADualityResult3.2.TheScaled-QMethodforSolvingthe^1OptimizationProblem3.2.1.AnAuxiliaryProblem3.2.2.RelatingtheAuxiliary
3、Problemtothe^1Problem3.3.Example4.RobustnesstoUnmodeledDynamics4.1.ConditionsforRobustnessGlossaryBibliographyBiographicalSketchSummaryInthischapterwepresentabriefdescriptionof^1robustcontrol.Wefirstmotivatetheuseofthe^1normandthenshowhowitisusedinformulating
4、acontrolproblemwiththeobjectiveofminimizingtheeffectofunknownbyboundeddisturbances.Thisleadstoformulationofthe^1optimalcontrolproblem,forwhichwepresentasolutionusingtheScaled-Qmethod.WethenaddresstheprUNESCO–EOLSSoblemofrobuststabilityandperformanceinthefaceo
5、fstructuredunmodeleddynamics.Hereweprovidesimpleandnon-conservativeconditionsforrobustnessthatareexpressedintermsofthe^1normsofthenominalsystem.SAMPLECHAPTERS1.IntroductionFeedbackcontrolisrequiredonlytocombatuncertainty.Indeedwithoutuncertainty,feedbackcontr
6、olhasnoadvantageoveropen-loopcontrol.Theubiquitouspresenceoffeedbackasacontrolstrategyinengineeringsystemsandnaturalsystemssuchasbiologicalsystemsisareflectionofthefactthatvirtuallyallsystemstobecontrolledhaveuncertaintyinoneformoranother.Thisstateofaffairsis
7、capturedsuccinctlybyAlbertEinstein’squote“Asfarasthelawsofmathematicsrefertoreality,theyarenotcertain;asfarastheyarecertain,theydonotrefertoreality”.Inengineeringsystems,it©EncyclopediaofLifeSupportSystems(EOLSS)CONTROLSYSTEMS,ROBOTICS,ANDAUTOMATION–Vol.IX–Ro
8、bustControl-MustafaKhammashisusefultocharacterizethisuncertaintyandtotrytoquantifyitseffectonsystemstabilityandperformance.Basinganycontroldesignonamodelofthephysicalsystemtobecontrolledm
