Estimation techniques for distributed parameter systems
type: Item
instance of: scholarly article
title: Estimation techniques for distributed parameter systems
zbMATH Open document ID: 0695.93020
published in: Systems \& Control: Foundations \& Applications
publication date: 1993-06-05T00:00:00Z
review text: The monograph deals with the identification of parameters in distributed systems. A typical class of problems under consideration are parabolic problems where the coefficient functions of the elliptic part have to be reconstructed from accessible state measurements. Problems of this type are ill-posed, with the degree of ill-posedness depending on many different factors. From the very beginning, the authors do not intend to give a comprehensive study of the nature of this ill-posedness. Following the lines of their personal research interests, they are mainly concerned with the aproximate solution of least squares formulations associated with the identification problem. To focus on the least squares approach has some justification from the fact that this technique is rather universally applicable and the most popular one. Another advantage is that the involved mathematical machinery is not overly complicated, so that the text remains accessible to readers from the applied sciences. The large number of numerical examples and the detailed description of the numerical algorithms are also very helpful for a better understanding of the theory. Moreover, while focusing on the least squares method, the authors also give an introduction to other recently developed identification techniques. In conclusion, although the more mathematically oriented reader might miss a reference to recently developed deeper analytical tools to treat the more delicate aspects of the inherent ill-posedness, the monograph is a welcome contribution to the identification literature. In particular, engineers and applied scientists will find it very useful for their practical purposes. The text itself is divided in seven chapters, followed by an appendix on the properties of spline spaces. Chapter I brings a detailed discussion of some typical identification problems arising from applications, while in Chapter II a number of well-known functional analytic tools are cited for later use. Chapter III is…
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 35R25
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93B40
zbMATH DE Number: 194855
zbMATH Keywords: distributed systems
zbMATH Keywords: ill-posed
zbMATH Keywords: least squares approach
zbMATH Keywords: parameter estimation
zbMATH Keywords: identifiability
zbMATH Keywords: stability
author: H. Thomas Banks
author: Karl Kunisch
reviewed by: Jürgen Sprekels
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 194855