An \(l_ 2\)-stable feedback structure for nonlinear adaptive filtering and identification
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.
scientific article; zbMATH DE number 987787
scientific article