Abstract
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