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1、HJBEquationsfortheOptimalControlofDi erentialEquationswithDelaysandStateConstraints,II:Veri cationandOptimalFeedbacksSalvatoreFederico,BenGoldys,FaustoGozziTocitethisversion:SalvatoreFederico,BenGoldys,FaustoGozzi.HJBEquationsfortheOptimalControlofDif-feren
2、tialEquationswithDelaysandStateConstraints,II:Veri cationandOptimalFeedbacks.2011.HALId:hal-00583124https://hal.archives-ouvertes.fr/hal-00583124Submittedon4Apr2011HALisamulti-disciplinaryopenaccessL'archiveouvertepluridisciplinaireHAL,estarch
3、iveforthedepositanddisseminationofsci-destineeaudep^otetaladi usiondedocumentsenti cresearchdocuments,whethertheyarepub-scienti quesdeniveaurecherche,publiesounon,lishedornot.Thedocumentsmaycomefromemanantdesetablissementsd'enseignementetdeteachingand
4、researchinstitutionsinFranceorrecherchefrancaisouetrangers,deslaboratoiresabroad,orfrompublicorprivateresearchcenters.publicsouprives.HJBEquationsfortheOptimalControlofDi erentialEquationswithDelaysandStateConstraints,II:Veri cationandOptimalFeedbacksSa
5、lvatoreFedericoyBenGoldyszFaustoGozzixApril4,2011AbstractThispaper,whichisthenaturalcontinuationof[14],studiesaclassofoptimalcontrolproblemswithstateconstraintswherethestateequationisadi erentialequationwithdelays.In[14]theproblemisembeddedinasuitableHilber
6、tspaceHandtheregularityoftheassociatedHamilton-Jacobi-Bellman(HJB)equationisstudied.Thegoalofthepresentpaperistoexploittheregularityresultof[14]toproveaVeri cationTheoremand ndoptimalfeedbackcontrolsfortheproblem.Whileitiseasytode neafeedbackcontrolformally
7、followingtheclassicalcase,theproofofitsexistenceandoptimalityishardduetolackoffullregularityofVandtothein nitedimensionalityoftheproblem.Thetheorydevelopedisappliedtostudyeconomicproblemsofoptimalgrowthfornonlineartime-to-buildmodels.Inparticular,weshowthee
8、xistenceanduniquenessofoptimalcontrolsandtheircharacterizationasfeedbacks.Keywords:Hamilton-Jacobi-Bellmanequation,optimalcontrol,delayequations,veri cationtheorem.A.M.S.SubjectClassi cation:34K35,49L2
