By Pieter Eykhoff
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Additional resources for Trends and Progress in System Identification. IFAC Series for Graduates, Research Workers and Practising Engineers
Sample text
N+1 n n+2 Ί 2η C M. ,Α η ' Ί Β], CA N,, n CA n-1 fact 1. , c m it follows that [ c p C , , , . . >cm>2îa^c^J - Lcx>c2» · · · »cmJ 't+2 y A t+3 of the Gedanken-Experiment with the state model H =C V H n+1 n 3. MINIMAL SINGLE-INPUT, SINGLEOUTPUT MODELS Firstly, to pass from the Gedanken-Experi ment to some minimal single-input, singleoutput (SISO) models, we start with some restrictions of the basic arrays. Secondly, in anticipation of the minimal SISO models and some transforms between them we present some facts.
Cxx t+l " " A t+1' = Ax,. + Bu,. "t+1 " ""t ' ""t and the Gedanken-Experiment on this model. Its carrier in the former sense was as follows: past y = A Bw where w is white zero-mean signal with intensity Q. We have to construct the filtered output y = Α-^Βηι(χ+ν) derived from y contaminated by white zeromean observation noise v which has intensity R. ). observed at times t+l+j The i-th column of the reachability matrix and the j-th row of the observability matrix were computed from the (i-l)th column and (j-1) row, respectively.
The ability to separate different objects is poor, thus the modeling brings no information. On the other end, with poor testing and an over-simplified characterization, the predic tability of the outputs, for any inputs, is not sufficient. Between these two extremes, there must be some "optimal1' model, capable of extracting from the measurements, all ^potential struc tural knowledge with the most discriminative structure. The more data we get, the more sophisticated the model we can afford. This entropy-like nature of the optimal model, makes modeling an endless problem.