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**An introduction to fuzzy control. With cooperation from Rainer Palm, Bruce Graham and Anibal Ollero. Foreword by Lennart Ljung.**
*(English)*
Zbl 0789.93088

Berlin: Springer-Verlag. xv, 316 p. (1993).

Writing this book, the authors’ intention was to “widen” the bottlenecks of broader exploitation of fuzzy control: – the need of a better and more systematic design and analysis methodology for fuzzy control applications and – the lack of well trained and experienced fuzzy control engineers.

The book is structured into 6 chaptes. The first chapter introduces the reader to the relevance of the use of fuzzy control. Among other concepts, the fuzzy knowledge controller (FKBC) is presented. In the second chapter (Mathematics of Fuzzy Control) those parts of fuzzy sets and fuzzy logic which are relevant for the design of FKBC are discussed. This chapter can be read without any knowledge of control theory.

In chapter 3 (FKBC Design Parameters) the principal parameters of FKBC and their relevance with respect to its performance is discussed. In chapter 4 (Nonlinear Fuzzy Control) the FKBC is considered as a particular type of nonlinear controller. PID like FKBC, sliding mode FKBC and linear filters with variable coefficients which are nonlinear functions of the state vector are presented. In chapter 5 (Adaptive Fuzzy Control) tuning and adaptation of FKBC-s concerning performance evaluation as well as main approaches to design are considered. Finally, in the 6th chapter (Stability of Fuzzy Control Systems) the stability problem is presented from the point of view of classical nonlinear dynamic systems theory. The book ends with an extensive bibliographic list of about 250 titles as well as with an index. The book is aimed at engineers from industry wanting to learn about fuzzy control and at university students needing lecture notes and references for their studies.

The book is structured into 6 chaptes. The first chapter introduces the reader to the relevance of the use of fuzzy control. Among other concepts, the fuzzy knowledge controller (FKBC) is presented. In the second chapter (Mathematics of Fuzzy Control) those parts of fuzzy sets and fuzzy logic which are relevant for the design of FKBC are discussed. This chapter can be read without any knowledge of control theory.

In chapter 3 (FKBC Design Parameters) the principal parameters of FKBC and their relevance with respect to its performance is discussed. In chapter 4 (Nonlinear Fuzzy Control) the FKBC is considered as a particular type of nonlinear controller. PID like FKBC, sliding mode FKBC and linear filters with variable coefficients which are nonlinear functions of the state vector are presented. In chapter 5 (Adaptive Fuzzy Control) tuning and adaptation of FKBC-s concerning performance evaluation as well as main approaches to design are considered. Finally, in the 6th chapter (Stability of Fuzzy Control Systems) the stability problem is presented from the point of view of classical nonlinear dynamic systems theory. The book ends with an extensive bibliographic list of about 250 titles as well as with an index. The book is aimed at engineers from industry wanting to learn about fuzzy control and at university students needing lecture notes and references for their studies.

Reviewer: L.Goras (Iaşi)

### MSC:

93C42 | Fuzzy control/observation systems |

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

03B52 | Fuzzy logic; logic of vagueness |

93C10 | Nonlinear systems in control theory |