An \(l_ 2\)-stable feedback structure for nonlinear adaptive filtering and identification
type: Item
instance of: scholarly article
title: An \(l_ 2\)-stable feedback structure for nonlinear adaptive filtering and identification
zbMATH Open document ID: 0869.93047
DOI: 10.1016/S0005-1098(96)00136-7
author: Ali H. Sayed
author: Markus Rupp
published in: Automatica
publication date: 1997-09-04T00:00:00Z
review text: An alternative look at the analysis and design of adaptive feedback for filtering and identification schemes is taken. One of the objectives of this work is to show how to reconcile, within a nonlinear estimation context, earlier developments in stable adaptive schemes with more recent developments in \(H^\infty\) design. The authors pose a nonlinear identification problem and a solution is proposed in terms of a feedback structure that consists of two steps. First, a linear approximation is employed and a standard \(H^\infty\)-filter design is carried out. Then, a feedback interconnection is introduced in order to guarantee an overall stable filter, under suitable conditions on the data and system parameters. The approach of this paper further clarifies the connections between Landau's and Feintuch's schemes in IIR modeling. Landau's scheme is shown to be a special case of a so-called a posteriori \(H^\infty\) filter, while Feintuch's algorithm is shown to be a special case of a so-called a priori \(H^\infty\) filter. Finally, it is remarked that the suggested feedback analysis can further be shown to provide an interpretation of most adaptive schemes in terms of a feedback interconnection that consists of two major blocks: (i) a lossless (i.e. energy-preserving) feedforward mapping and (ii) either a memoryless or a dynamic feedback mapping.
reviewed by: Tzvetan Semerdjiev
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 987787
zbMATH Keywords: adaptive feedback
zbMATH Keywords: nonlinear identification
zbMATH Keywords: \(H^ \infty\)-filter
zbMATH Keywords: lossless
zbMATH Keywords: feedforward mapping
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 987787