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PEo PLE HAVE DEVELOPED MODI FIED COST FUNCTIONS OF THE FoRM 0)(⊥+ FRsτTERA: STANDAR△cosT EcoNO TERM: PROVIDES A MEASORE OF THE DMPLEXITY OF THE mooEL s> TYPICALLY HAVE WITH MODEL SIZE INCREASE,6υ刂↑ 今 GIES Us A wAy7TA0工AN0 VEMENT5 TN VN AGAINST MoDEL COMPLEYITY ● STAND丹R0CRtT∈R升 AKAIKE INF. CRITERION (AIc) MIN DESCR\PTION LENGTH(MOL) UN: LOGN d0wENS(o小0Fe 83 ECTIVE Now:AN了 d, e →FRF1以ED MN了 PLOT J Vs. d AND SELECT LOWESTVALVE 丹cEss1 BLE FoR ARX MODELS工 N ARX STRUC.A
2 STATE SPACE foRM DISCRETE TIME MODELS WRITTEN IN TERMS 0FSτ ATE SPACE0 FFERENCE ERUATIo心 k升xk+Buk K20 K K A55MEX。=0 CONSIDER RESPONSE TD A UNIT DISCRETE 工MULE(工E. k·1 工FFK=0 RESPONSE Y。CX。- ·CX、=cB x,=A6 Y2·C2cA8×z=8 YK Cab K> THE TERMS h=CAB ARE CALLED THE MARKoV PARAMETERS OF THE SYSTEM 今 THE MARKOV PARA飞 ERs ARE THE VALvE OF THE 0ISCRETE-TIME IMPULSE RESPDNSE SEE KAILATH CHEN
HANKEL MATRiX AN IMPORTANT MATR升 SSoCIAT∈0mH MARKov PA RAME TE Rs ELE比 ENTs oF THE HAAKEL MATRIX At毛 THE MARK0 N PARAMETERS-Co小sTNT什LG ANTI-D,AGoNALS R∈ALL工 MPoRTANT1 NoTE THAT8 [8A6] B AB CAB CAB MC - CONTROLLABILITY MATRIX OBSERVABILTf MATRIX CLOSE CONNECTION BETWEEN 8ETEE小 HANKEL MATR AND M。,A
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