一類非線性分布參數(shù)系統(tǒng)的可控性、穩(wěn)定性及其最優(yōu)控制.pdf

1、廣西大學碩士學位論文一類非線性分布參數(shù)系統(tǒng)的可控性、穩(wěn)定性及其最優(yōu)控制姓名：劉海員申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：潘健2002.5.1一——————————————————————————————————————～一——一[墮查蘭堡圭堂堡絲塞ControllabilityStabilityandItsOptimalControlofAClassNonlinearDistributedParameterSystemABSTRAC

2、TInthispaper，westudyaclassofnonlineardistributedparameterasfollows尸OQ丁(xt)_D△Q(圳t壩，，Q(蚺m，呦(列)∈QX[c0，。。)t、i)1硝z，∈S2xf。。lily(x，f)=g(t，Q(x，f))TheinitialconditionQ(x，0)=Q(z)z∈Q，Atfirstwetransformitanabstractevolutionequation

3、：』掣叫f)Q(f)F(Q，f)lQ(o)=Q。(2)Usingthetheoryofsemigroupsofoperators，wefindthemildsolutionofsystem(1)andthesolutionisuniqueConsideringcorrespondinglinearsystem：∞掣H八D㈣wefollowthesufficientandnecessaryconditionsofsystem(2)from

4、thecontrollabilityofsystem(3)。Sothesufficientandnecessaryconditionsofsystem(2)isobtained。Wediscussthestabilityconditionsofsystem(1)Onthebaseofitscontrollability。Atlastwestudythenecessaryconditionsofoptimalcontrolproblemo

5、nthesystem，andapplyingtovariationtheoryweacquiretheadjointequationwhichtheadmissiondual—controlsaresatisfied。KEYWORDS：nonlinear；abstractevolutionequation；distributedparametersystem；controllabilitystability；optimalcontrol