QR分解技术在递推系统辨识中的应用

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1、北京交通大学硕士学位论文QR分解技术在递推系统辨识中的应用姓名：孙延鹏申请学位级别：硕士专业：控制理论与控制工程指导教师：程轶平20080601ABSTRACTABSTRACT：Modemcontroltheoryconsistsofsystemidentification，stateestimationandcontroltheory．Systemidentification，partofsystemmodeling,includesidentifyingthestructureofmathematica

2、lmodelandestimatingparametersofmathematicalmodel．Itplaysakeyroleinbothrealityandtheorytoidentifythestructureandparametersofsystems．TheLeastSquareMethod(LS)，笛allimportantapproachofsystemparameteridentification，haSbeenwidelyappliedtonumerousfieldsandoccasion

3、s．RealizationmethodofLSisimprovedtoaccelerateidentificationbymeansofQRdecompositioninthispaper．QRdecompositionoftheblockHankelmatrixisobtainedthoughGIVENStransformation，onthebasisofwhichtherecursiveidentificationforsystemparametersisderived．Inthispaper,the

4、followingaspectsaremainlystudied：Firstly,theLeastSquaremethodofsystemparametersidentificationisstudied，andbyanalyzingtheoutputequationmodel，theLeastSquareestimationresultcanbegot；thentheQRdecompositionisintroducedtomakeupforitsdisadvantagessuchaslowprecisi

5、onandefficiencybesidesitsbadnumericalstability．TheQRdecompositioncanbeimplementedbyseveralmethods，bycontrastofwhichthesimplest2x2GIVENStransformationischosen够theavenueofdecomposingtofitforthealgorithm．Basedonthis，themodifiedrecursiveidentificationalgorithm

6、forSingle-Input-Single-Output(SISO)systemisderivedandappliedtothecaseofcontainingforgettingfactonThedata-drivenproblemisalsodealtwithindetaillater．ByanalyzingthemathematicalmodelofMIMOsystemandchangingtheformofthetransformfunction，theMulti—Input-Multi—Outp

7、ut(MIMO)systemCallequivalentlybereplacedbyseveralMulti—Input-Single-Outputsubsystems．ThustheparametersidentificationforMIMOsystemcallbeimplementedbyidentifyingthesubsystems．Theinputsalethesameforallsubsystems，SObydealingwiththeinputdataandcitingtheresults，

8、therecursiveidentificationforsubsystemparametersCanherapidlyderived．ThentheidentificationforMIMOsystemparameterscanbeobtainedrapidlybythesubsystemmethod，thedatadrivenproblemalsosolvedeffectively．Consideringth