隨機(jī)發(fā)展方程最優(yōu)控制問題的研究.pdf

1、華中科技大學(xué)博士學(xué)位論文隨機(jī)發(fā)展方程最優(yōu)控制問題的研究姓名：周建軍申請學(xué)位級別：博士專業(yè)：概率論與數(shù)理統(tǒng)計指導(dǎo)教師：劉斌20110505華中科技大學(xué)博士學(xué)位論文AbstractStochasticevolutionequationsarethepopulartopicsofdynamicsresearch.BasedontheexistedliteraturesthisthesisstudiesthenonlinearKolmogove

2、quationsassociatedwithstochasticdelayevolutionequationsapplicationstostochasticoptimalcontrolproblem.MeoverthisthesisconsiderstheoptimalcontrolproblemfstochasticevolutionequationsstochasticdelayevolutionequationsinHilber

3、tspaces.ThisPh.D.thesisisdividedintofourchapters.InChapter1weintroducethehisticalbackgroundthecurrentsituationthemainresultsofthisthesis.InChapter2nonlinearKolmogovequationsitsapplicationstooptimalcontrolfstochasticdelay

4、evolutionequationsarestudied.FirstlytwobasicLemmasareprovedtoensurethatthenonlinearKolmogovequationsbewelldefined.ThenfwardbackwardsystemisconsideredregulardependenceonparametersMalliavindifferentiabilityareshowedwedefin

5、eadeterminedfunctionv:[0T]C→Rbythesolutionofbackwardstochasticdifferentialequations.WeprovedthatthefunctionvisaclassicalsolutionofthenonlinearKolmogovequationsifvissufficientlyregular.Meoverundertheassumptionsofthischapt

6、erweprovethatthereexistsauniquemildsolutionvofthenonlinearKolmogovequationthefunctionvhasthepropertyofassociatedTheem.Finallyasanapplicationanoptimalcontrolofstochasticdelayevolutionequationsisgiventoillustrateourresults

7、.Byconstructinganoptimalfeedbackweobtainoptimalcontrolshowthatvisthevaluefunction.Theresultsisnew.InChapter3weconsideranoptimalcontrolprobleminwhichthecontrolledstatedynamicsisgovernedbyastochasticevolutionequationinHilb

8、ertspacesthecostfunctionalhasaquadraticgrowththecontrolprocesstakesvaluesinaclosedset(notnecessarilycompact).ThebackwardstochasticdifferentialequationcrespondingtoourcontrolproblemhasaquadraticgrowthintheZvariable.Themon

9、otonestabilityfthisclassofbackwardstochasticdifferentialequationsinfinitedimensionalhasbeenobtainedinthecaseofboundedterminalvalue.BythesimilarapproachwecanshowthattheresultsalsoholdtrueiftheBSDEisdrivenbyacylindricalWie