This is a comprehensive book discussing several methods for the
identification of nonlinear systems. Identification is extremely
relevant in applications and only recently has much ongoing research
addressed the pressing problem of identifying systems with
nonlinearities. In this respect, the book is timely as it is a
collection of results from many different areas in applied
science, ranging from linear optimization techniques to fuzzy logic and
nonlinear adaptive control.
The declared aim is `to provide engineers and scientists in
academia and industry with a thorough understanding of the
underlying principles of nonlinear system identification'. At the
same time, the author wishes to enable users to apply the
methods illustrated in the book.
The book is well structured and divided into four distinct parts.
The first part is entirely devoted to an overview of the main
optimization techniques for nonlinear problems. Least squares
methods and other classical strategies such as general
gradient-based algorithms are discussed. While the presentation is
clear, it is too wordy at times, making it difficult to appreciate
the key issues involved. A set of diagrams and summarizing tables
is included, though, to improve the overall clarity and highlight
similarities and differences.
The second part is mostly devoted to static models such as linear,
polynomial and look-up table models. The main emphasis is on
neural networks and fuzzy logic. The results are clearly expounded
but the aim of giving a general overview of too many different
approaches in some cases hampers the clarity of the exposition.
Neuro-fuzzy models are presented in chapter 12 and further
detailed in chapters 13 and 14 where local linear Neuro-Fuzzy
models are discussed. In particular, chapter 13 focuses on methods
proposed by the author. Despite their usefulness, I found that the
choice of dedicating two entire chapters to such methods causes a
slight imbalance in the presentation. Up to chapter 13, the
discussion is quite well balanced and different methods are given
the space needed to expound the main results. Unlike the other
strategies, in my view, local neuro-fuzzy approaches are treated
in far too much detail. This is beyond the scope of the book,
which is that of giving a general balanced overview of all
possible results. A summary of the second part is reported in
chapter 15 where the author reinforces the view that local
neuro-fuzzy methods should be more widely applied for static
modelling problems.
Dynamic Models are the subject of the third main section of the
book. Linear dynamic system identification is discussed in
chapter 16, where time series models are presented together with
multivariable methods and other linear approaches. Nonlinear
dynamic systems are considered in chapter 17 and are followed by
classical polynomial approaches in chapter 18. Neural and fuzzy
dynamic models are treated together with local neuro-fuzzy dynamic
systems in the remaining chapters of this third part. Again
particular emphasis is given to local neuro-fuzzy systems which
have been the subject of research and development by the author.
Unfortunately, this part does not include a chapter dedicated to
summarizing the main results expounded. It must be noted though that
many diagrams and schematics do help in highlighting the main
results. Nevertheless, an extensive summary such as the one
included at the end of the second part would have been useful.
As I have indicated, Nelles has certainly described an extensive
number of results in the book. On the other hand, more recent
methods based on novel developments of Nonlinear Dynamics such as
nonlinear time series analysis, which have been successfully used
to identify nonlinear systems,
have not been included in the book. I hope they will be
incorporated in later editions, as they have the potential to play
an important role in the identification of complex models.
Applications are discussed in the fourth and last part of the
book. The problems presented are interesting but again it becomes
apparent that local linear neuro-fuzzy methods are somehow the
author's preferred method. This bias, which might well be motivated
by the author's experience, should in my view be
counterbalanced by applications showing the use of other methods.
Some are indeed included in the final chapters of the book but I
would have liked to see a few more problems.
Two appendices recall some useful results from linear algebra,
vector calculus and statistics and are well suited to a general
readership. An impressive reference list of more than 400 items
completes the book, representing an invaluable starting point for
further research and details.
As mentioned in the Preface, throughout the book Nelles tries to
keep the mathematical description to a basic level. This
indeed makes the textbook accessible to a wider audience. Unfortunately,
it also results at times in lengthy, wordy descriptions of the
most intricate approaches. As a consequence, users who wish to
apply some of the methods discussed to problems that interest
them will often find that they need to look up further details from
other sources. In this respect, the extensive reference list at
the end of the book will certainly be helpful. Despite this
disadvantage, the book is certainly an invaluable archive of
available strategies for nonlinear system identification, which
will undoubtedly help readers with the choice of the particular
method to use.
In conclusion, as I have indicated, I found the book a
well-packaged overview of the main results concerned with
nonlinear system identification. But I believe that the
description is wordy at times and not rigorous enough. Contrary to
what is stated in the Preface, I believe that rather than being a
self-contained book, readers will undoubtedly need to look up
further references to be able to make use of the methods
illustrated. On the other hand, the book should be a useful
reference for students. It certainly deserves to be included in
the reading list of any course on nonlinear system identification
and optimization.
Mario di Bernado