Biomedical Engineering - Bioengineering of Physiological Control Systems

System Identificaton Open Loop

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IDENTIFICATIONfromDATA TOPREDICTtheOVIPVIhavingpostObservationsontheINPOT/OvipvtrelationshipBUPREDICTIONgnaspsonlytheOBSERVABUEandPREDICTABUEpartoftheVariable (yprd(t)):snnlessyct)isaDETERMINISTICSIGNAL,theirispartofyct)thatisUNPREDICTABLE→theRESIDUALERROR(ect) ) 2APPROACHESOPENLOOPCLOSEDLOOP9INCONSISTENTIinPHYSIOLOGY,ult)andelt)areassumedtobeUNCORRELATEDault)andect)becomescorrelataduetotheFEEDBACKallphysidogicalregulationsect)mayct)-ult)areFEEDFORWARD+FEEDBACK!!HEREtheCAUSALRELATIONSHIPhastobeCERTAIN^WecandeadwiththisproblembyanalyzingtheCANALRELATIONS PARAMETRICIDENTIFICATION AUOWSinmamyCasasaGOODCLOSED-COOPSYSTEMIDENTIFICATION,ButitisbasedontheANALYSISofCAUSALRELATIONSassumptionabouttheTEMPORALORDERoftheevents>PASTult)Causesyct)andthepostofyct)Causesult)ConverselyisalmostunfeasiblewithSINUSOIDS,sinceinthatCeasethisTEMPORAL/causaleRELATIONCan'tbeSdvedmaFOURIERMETHODSthePROBLEMofCAUSALITYPROBLEM:IdentitytheCAUSALRELATIONSHIP→whatistheINPUTandwhatistheOVIPVIbetweeu2correlatoVariables?USUALLYIt'snotdifficultfromdatatodetectCORRELATION,ButAlientheiristheproblemofdetermininowhatistheCAUSEandwhatistheEFFECTanditisImportanttoKelpinnindthatinsoneCasas(especiallyinclosedloop)theTIMEFactorisMEANINGUESS(Cynicevolution)orcanbeeuenMISLEADINGTOASSUMEanINVERSEDCAUSAUTYMearnstoMISTAKEtheFEEDFORWARDACTIONforFEEDBACKandviceversa,sotoconsideriimcorrectlyaPREVALENCEofFEEDBACKACTIONontheFEEDFORWARDACTIONerGCW)APPROXIMATION(thatwasintroduceinPUPILDIMENSIONREGULATION)thatcanbemadetosimplifytheFlu)=1+GCWIHCW)@CONTROLBWmaFeedforwandactioniseffectivesotheLOOPFUNCTIONisnotrequiredGCWIHCS)«1SYMMETRIC,TOEPLITZsrue=autocorrelazionewithelagcupo,.a.→ ÷... :* , [ .÷.. " " , ruic=Gov(Uci),leciti))Mci)=(y(i-1)...yli-na))••F-ha INPUT + OVIPUT Predictionisbasedexclusive(yonPostObservationsoftheoutputARwithexogenousinput(ARX) M(i)=(Uci-K)...Uci-K-nota)y(i-1)...y(i-ha))••F-thatNbBESTESTIMATION:THECLOSERTOTHEWNCASETHEBETERdet(Covcm))isMaxeB-= ( carmi)"→Po×^soinANYCASEtheClosetTHEINPVItodellCalm))ifUri2=10aWNthebelterarethelowest1ifitisnotpossibleatleastaBROADBANDWIDTHSOBESTCASEIFult)~WNCO.it)$Calm) =/È "È)=IImomt)=impulseasirregolari(Lassperiodica)aspossible→Poissondistribution(asseemforRsa )PEMIDENTIFICATION→fromsampieddata→DISCRETEDOMAINnoIdentificationofTFCZ)GENERALSTRUCTURE kkstb ect),H(z)y=G(z)µ+H(z)e=B")u+C'E)Alz)FCZ)Alz)☐(Z)eult),✓+Ylt)Ge);-Alz)y =BA)u+"£)eFCZ)Dtt)Alz)=1+oraÈ+...tanaÈ""→COMMONPOLEStobothDETERMINISTICandSTOCHASTICPARTSB.(z)=È"(b,+b,È+...+buiaÈ"")maZEROESoftheDETERMINISTICPARTf-(E)=1+faÈ+...tfn,È"maPOLESoftheDETERMINISTICPART((Z)=C,E'+...+(niti"maZEROESoftheSTOCHASTICPART☐(Z)=1+d,È+...+dn,È'→POLESoftheSTOCHASTICPART PARAMETRICESTEEMEVALUATION in FREQUENCYDOMAIN >istheestimatedparametricomodelCONSISTENTandACCURATE?istheTRUEMODELINCLUDEDintheESTIMATEDMODEL(=doesthemodeldescoibealltheDETERMINISTKSOURCESofVA R I AT I O N?)(NOBIAS) CONS / STENCY :(INPRACTICE)CONSISTENCYcanbeprovenbySIMULATIONaparametricomodelestimatedfromDATAissaidtobeconsistente1ModelIdentificationusingult)~WN(0,72)tohaveifwithaPERSISTENTLYEXCITINGINPVI(a.WN,oratleastbroadBW)theBESTESTIMATIONonPARAMETERSÈtheestimatedmodelconvergetotheTRUEMODEL2Te s ttheobtainedmodelsimulatimgREALCONDITIONSult)~realphysidogicalINPVISIGNALult)-WN(0,22)