Advances in Theory and Applications : System Identification by Cornelius T. Leondes

By Cornelius T. Leondes

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Additional info for Advances in Theory and Applications : System Identification and Adaptive Control, Part 2

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Tant for numerical reasons. It is impor­ It guarantees that if the data are informative enough, the parameter estimation problem will be well posed, since different Θ yield different I/O properties. The definition we have adopted is by no means unique. , [18], [23], [35]). Other definitions are based on the Kullback-Leibler information or on the theory of estimable functions Csee [35,36]). Notice finally that the term "structural identifiability" has a different meaning in econometrics [25]. IV.

This particular V is called the generic neighborhood, because generically a system will have Kronecker indices n, , , + 1 = · · · = η p + 1 for 1 = ··· = n q = η q+1 some q. Hence, in practice, the generic neighborhood (and its corresponding canonical parametrization) is sufficient to repre­ sent almost any system. However, other nongeneric y's (and their corresponding parametrizations) might be preferred for numerical reasons. For the generic μ, d(y) = n(p + s ) ; the other V are mapped into spaces of lower dimension.

An alternative is to cover S(n) by disjoint sub­ sets V , which can again be coordinatized by nonoverlapping coordinate systems. These will give rise to the somewhat sim­ pler canonical SS, MFD, and ARMAX forms. Definition 3. the subset of U for which the μ rows (34) specified by μ are the first n linearly independent J We call V μ rows of H, [K]. i, °° Since the row r. +1n ' l basis rows above it, (35) is replaced by n. P il :. +l ^ zL ijl jl 1 j=l 1=1 where n. , p, if i < j, y — /\ min(n. ) (39) if J ' i > j.

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