偏微分網(wǎng)絡(luò)的反問題.pdf

1、天津大學(xué)博士學(xué)位論文偏微分網(wǎng)絡(luò)的反問題姓名：王雷申請學(xué)位級別：博士專業(yè)：控制科學(xué)與工程；控制理論與控制工程指導(dǎo)教師：許跟起201104ABSTRACTInverseproblemofpartialdi髓rent謝equationsisatheoreticallych止1en西ngtopicandhasV甜iousapplicationbackgroundsIthasbeenintellsivelydiscussediIlthepastt

2、enye盯sComp盯ed耐ththeidenti丘cationofthep扣ramete：r0fnetWorksystems，thereareonlyafewUteraturesstudyingtheidentmcationofthestructureofthenetworl【sAsf打asweknow，thephysicalstructureoftreesh印ednetworbcanbeidenti丘edbyitsspectraHo

3、wever，itisdi伍culttoprovideareasonablewaytoident毋thestructureofcompleXnetWorl【s，such嬲theonescontainingp盯aUeledges，loopsorcircuitsThereasonisthattheident進cationofthe8tructureofcompleXnetworksi8non1ine盯andthatthe8esyste腳don

4、otpossesseXactobservabintyandeXactcontrollabilityAvdoninregardedt地problemasanopenquestionInthisthesis，Ⅵreim髑tigatethestmctllrerecon8tructionofcompleXne擁的rl【scontainingcircuits，paralleledgesandloopsbyintroducingres01ventm

5、ethodThemaLinresultsareasfbllowrs：1Wbpresentthemodelof1一dcompleXwavenetworl【s耐thcontinuousplacementsWbfirstde丘neconti肌ous缸1ctionongr印h，aJldthendesc曲ethedyn枷calbehaviorofthenetWorl【s講thWaveequations，bouIlda唧eonditionsandi

6、nteriorconnectionconditionsanddynamicaLlconditio璐2Bytheanalysisofthecorrespondingch盯acteristicequatioIlsoft11reebausicnetwDrl【s，namelyseriallyconnectedwa№netwDrk，networkonacircuit，andsta卜sh印ednetwork，weobt豇nthemlmberofth

7、eedgesofthenetwork，andmea舯lrhile百vethecharaucteristicequationofgeneralnetwDrb3Wbintroducetheres01ventmethodandpresentthee印ressionoftheGreenfhnctionmatr恢ofwaⅣenetworl【sbyconstructionW色provethattheGreenfunctionmatr政andtheb