無(wú)界區(qū)域上線性拋物系統(tǒng)的能控性問(wèn)題.pdf

1、華中師范大學(xué)碩士學(xué)位論文無(wú)界區(qū)域上線性拋物系統(tǒng)的能控性問(wèn)題姓名：張志飛申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：汪更生20050501⑧碩士學(xué)位論文MASTER’STHESISAbstractInthispaper，weshallstudytheexactnullcontrollabilityandapproximatecontrollabilityofthecoupledlinearparabolicsystemasfollow

2、swhenthecontrolforceactsonasin斟e(cuò)equation；f軌=△掣alya2zJ魂=Azbly622地，l可@，￡)_z(墨t)=0【g(。，0)=yo(Z)，。(z，0)=zo(x)inQT=Q(0，T)，in劬=Q(0，T)，。、on島：觸(0，r)，(11)inQwhere‘1isanopenandunboundedsetof艫withboundary8Qof02uniforrely“isanopenan

3、dnonemptysubsetofQsuchthatQ＼uisboundedxuisthecharacteristicmnctionofu，System(11)issaidtobeapproximatecontrollableintimeT0，ifforanyfinalstate(Yl，ZI)∈L2(Q)L2(Q)and￡0，thereexists五∈三2(“(0，r))suchthatthesolutionof(1I)satisfie

4、s(弘(‘，T)一yl，2(，T)一z1)liL。(∞S￡(13)System(11)issaidtobeexactnullcontrollableintimeT0，ifforany(Y0，ZO)∈L2(Q)L2(Q)，thereexistsf∈L2(u(0，))suchthatthesolutionof(11)satisfies(黟，z)(t，T)=0aeinQ(141Themaindifficultyofthisworkistoes

5、tablishobservabilityinequalityFirst，wegettheCarlemaaestimateThenbasedOnit，theobservabilityin—equalityisobtainedFinallywegetthecontrollabilityofthesystemTheaboveproblemswillbediscussedasthefollowingfourparts：P盯t1Introduce