含有一個(gè)控制的擬線性拋物系統(tǒng)的能控性.pdf

1、華中師范大學(xué)碩士學(xué)位論文含有一個(gè)控制的擬線性拋物系統(tǒng)的能控性姓名：何紅英申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：汪更生20050501◎碩士學(xué)位論文MASTER’STHESISAbstractTheaimofthisarticleistoproperthecontrollabilityofthefollowingquasi—linearparabolicsystemwhereY，zarethestatesandu∈L∞(u(o，T))

2、isthecontrolfunctionwhichactsonthesystemthroughthesubsetu(90，z0)isgivenfunctionin(W1’。。(Q)n硪(rid2Systemissaidtobenull—controllable，ie，foreach(Y0，匈)，thereexistsacontrol“∈三∞(Q)，suchthatthesolution(y，石)∈(三∞(o，T；L2(f2)))2sat

3、isfies(Y，z)(，T)=0innSystemissaidtobeapproximatelycontrollableinL2(Q)三2(Q)，ie，foreach(Yd，Zd)∈L2(Q)L2(Q)andanyE0，thereexistsacontrol讓，suchthattimsolution(Y，。)∈(L。(o，；鏟(Q)))2satisfies(Y，z)(，T)一(ya，Zd)IIL2≤EinQThenonlinearte

4、rms／(x，t，Ⅳ，z，vy)，9(z，t，Y，z，Vy，Vz)arelocallyLip—schitzcontinuousMoreoverthecontrolforcesactOnasingleequationofthesystems，controllingasystemwithaminimumnumberofforcesorbyfcIrcessatisfyinganalgebraicoranyothertyperelationis

5、acommonproblemInthecontroltheoryThekeyingredientsofourproofareglobalCarlemaninequalityandObservabilltyestimateforthelinearizedsystemandthentouseafixedDoiHttheoremThemaindifficultyistoprovetheObservabilityestimatefortheIi