In control engineering, signal processing, and neural network modeling, researchers explore mathematical models for the prediction of system states under a certain operational environment, for estimation of the system parameters, or for simulations. Following Zadeh and Ljung’s definition, parameter identification consists of data, model, and equivalence criteria.

This book discusses a variety of topics related to parameter identification. All of the authors have worked in control theory for years, and each holds many patents; their knowledge and experience is an essential contribution to the field.

The book is organized into six chapters. Following an introduction, the remaining chapters address topics including information measures, information theoretic parameter estimation, system identification under minimum error entropy criteria, system identification under information divergence criteria, and system identification based on mutual information criteria. Common measures, such as least square, entropy, mutual information, information divergence, Fisher information, or the proposed information rate, are introduced. Subsequent chapters discuss criteria such as Bayes estimation, minimum error rate, and minimum error entropy. The last three chapters propose system identification models under the equivalence criteria introduced at the beginning, in quite a simple way.

All of the models are supported with detailed calculations, codes, tables, examples, and kernels to make the concept clear for the reader. The theorems are followed by proofs, and almost all of the variables used in the formulas are defined, something I cannot say about many other mathematical books.

However, neither the system nor the parameters are defined. It appears that the authors hand that task over the reader. In other words, it is up to the reader to know how and where to employ the mathematical models described. Pragmatically, some may find the book’s content very useful and practical, with the potential for application in a variety of fields, not necessarily just engineering. On the other hand, readers with more general knowledge may find it no more useful than other specialized mathematical material.

I found this book timely, interesting, and very well written. Readers can learn about estimation methodologies, the art of proof, and identification of the parameters assumed by the system architect or designer. The proposed approach promises to support any system with a broad variety of parameters selected for a particular analysis.