000135173 001__ 135173
000135173 005__ 20190331192640.0
000135173 0247_ $$2doi$$a10.1109/TAC.2009.2034199
000135173 02470 $$2ISI$$a000272601600009
000135173 037__ $$aARTICLE
000135173 245__ $$aIdentification and the information matrix: how to get just sufficiently rich?
000135173 269__ $$a2009
000135173 260__ $$c2009
000135173 336__ $$aJournal Articles
000135173 520__ $$aIn prediction error identification, the information matrix plays a central role. Specifically, when the system is in the model set, the covariance matrix of the parameter estimates converges asymptotically, up to a scaling factor, to the inverse of the information matrix. The existence of a finite covariance matrix thus depends on the positive definiteness of the information matrix, and the rate of convergence of the parameter estimate depends on its “size”. When the system is not in the model set, the nonsingularity of the information matrix at all identifiable values of the parameter vector is a necessary condition for the asymptotic convergence of the identification algorithm. The information matrix is also the key tool in the solution of optimal experiment design procedures, which have become a focus of recent attention. Introducing a geometric framework, we provide a complete analysis, for arbitrary model structures, of the minimum degree of richness required to guarantee the nonsingularity of the information matrix. We then particularize these results to all commonly used model structures, both in open loop and in closed loop. In a closed-loop setup, our results provide an unexpected and precisely quantifiable trade-off between controller degree and required degree of external excitation.
000135173 6531_ $$aIdentifiability
000135173 6531_ $$ainformation matrix
000135173 6531_ $$ainput richness
000135173 6531_ $$atransfer of excitation
000135173 700__ $$aGevers, M.
000135173 700__ $$aBazanella, A. S.
000135173 700__ $$aBombois, X.
000135173 700__ $$g133818$$aMiskovic, L.$$0240448
000135173 773__ $$j54$$tIEEE Transactions on Automatic Control$$k12$$q2828-2840
000135173 8564_ $$uhttp://ieeexplore.ieee.org$$zURL
000135173 8564_ $$uhttps://infoscience.epfl.ch/record/135173/files/GEVERSM-07-197-Final.pdf$$zn/a$$s1380427
000135173 909C0 $$xU11422$$0252131$$pLCSB
000135173 909CO $$ooai:infoscience.tind.io:135173$$qGLOBAL_SET$$pSB$$particle
000135173 937__ $$aLCSB-ARTICLE-2009-004
000135173 973__ $$rREVIEWED$$sPUBLISHED$$aOTHER
000135173 980__ $$aARTICLE