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Identification and rational L2 approximation A gradient algorithm

✍ Scribed by Laurent Baratchart; Michel Cardelli; Martine Olivi

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
471 KB
Volume
27
Category
Article
ISSN
0005-1098

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✦ Synopsis

Al~traet--This paper deals with the identification of linear constant dynamical systems when formalized as a rational approximation problem. The criterion is the 12 norm of the transfer function, which is of interest in a stochastic context. The problem can be expressed as nonlinear optimization in a Hilbert space, but standard algorithms are usually not well adapted. We present a generic recursive procedure to find a local optimum of the criterion in the case of scalar systems. Our methods are borrowed from differential theory mixed with a bit of classical complex analysis. To our knowledge, the algorithm described in this paper is the first that ensures convergence to a local minimum. *

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