資源描述：
《application to systems and control》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫(kù)。
1、Chapter6APPLICATIONTOSYSTEMSANDCONTROLAssumeacontrolsystemdependsonaparameterandthesystemoperationreachesitsidealstatuswhentheparameterequalssomeSinceisunknown,wehavetoestimateitduringtheoperationofthesystem,which,therefore,canworkonlyontheestimateofInotherwords
2、,therealsystemisnotundertheidealparameterandtheproblemistoon-lineestimateandtomakethesystemasymptot-icallyoperatingintheidealstatus.ItisclearthatthiskindofsystemparameteridentificationcanbedealtwithbySAmethods.Adaptivecontrolforlinearstochasticsystemsisatypicale
3、xampleforthesituationdescribedabove.Ifthesystemcoefficientsareknown,thentheoptimalstochasticcontrolmaybeafeedbackcontrolofthesystemstate.Thecorrespondingfeedbackgaincanbeviewedastheidealparameterwhichdependsonthesystemcoefficients.Inthesetupofadaptivecontrol,sys
4、temcoefficientsareunknown,andhenceisunknown.Theproblemistoestimateandtoprovethattheresultingadaptivecontrolsystembyusingtheestimateasthefeedbackgainisasymptoticallyoptimalastendstoinfinity.InSection6.1theidealparameterisidentifiedbySAmethodsforsystemsinagenerals
5、etting,andtheresultsareappliedtosolvingtheadaptivequadraticcontrolproblem.TheadaptivestabilizationproblemissolvedforstochasticsystemsinSection6.2,whiletheadaptiveexactpoleassignmentisdiscussedinSection6.3.Anadaptiveregulationproblemfornonlinearandnonparametricsy
6、stemsisconsideredisSection6.4.289290STOCHASTICAPPROXIMATIONANDITSAPPLICATIONS6.1.ApplicationtoIdentificationandAdaptiveControlConsiderthefollowinglinearstochasticsystemdependingonparam-eterwhereandareunknown.TheidealparameterforSystem(6.1.1)isarootofanunknownfun
7、ctionThesystemactuallyoperateswithequaltosomeestimatefor,i.e.,therealsystemisasfollows:Forthenotationalsimplicity,wesuppressthedependenceonthestateandrewrite(6.1.3)asTheobservationattimeiswhereisanoiseprocess.From(6.1.5)itisseenthatthefunctionisnotdirectlyobserv
8、ed,butitisconnectedwithasfollows:whereisgeneratedby(6.1.1).Letbeasequenceofpositivenumbersincreasinglydivergingtoinfinityandletbeafixedpoint.Fixinganinitialvaluewerec
