The technologies of fuzzy systems and fuzzy controllers, in particular, have been applied with great success to numerous real world applications. The number of entries in the INSPEC database with keywords “fuzzy mod- ing” and “fuzzy control” dated 1969–2007is 1,541 and 9,728, respectively. In spite of the evident progress reported in terms of concepts, algorithmic - velopments and engineering practice, there are still a number of challenging and highly relevant problems. Unfortunately, the existing publications are rather silent when it comes to reporting comprehensive solutions to them. The two challenges become particularly apparent and have been triggeredby the growing complexity of the applications. The ?rst evident challenge we are faced with is the curse of dimensionality. Rule–based systems and fuzzy rule–based systems are quite a?ected by this phenomenon especially when tackling problems of high dimensionality. The second one concerns a way of constructing fuzzy models which are accurate yet highly interpretable. The author of the monographhas focused on these two vital problems and o?eredan interesting,originaland practically relevantinsight into their so- tions.Whendealingwithfuzzymodeling,thebookfocusesonabroadclassof Takagi–Sugeno–Kang (TS) fuzzy models – a highly legitimate choice given a wealthof literature onthese constructs and a greatdeal of their applications. Furthermorethe TS fuzzy models havebeen asubject ofnumerousanalytical studies which have resulted in a series of interesting ?ndings. This situation stands in a deep contrast with the most studies carried out in the realm of fuzzy control where analytical methods are not very common.
This book is focused on mathematical analysis and rigorous design methods for fuzzy control systems based on Takagi-Sugeno fuzzy models, sometimes called Takagi-Sugeno-Kang models. The author presents a rather general analytical theory of exact fuzzy modeling and control of continuous and discrete-time dynamical systems. Main attention is paid to usability of the results for the control and computer engineering community and therefore simple and easy knowledge-bases for linguistic interpretation have been used. The approach is based on the author’s theorems concerning equivalence between widely used Takagi-Sugeno systems and some class of multivariate polynomials. It combines the advantages of fuzzy system theory and classical control theory. Classical control theory can be applied to modeling of dynamical plants and the controllers. They are all equivalent to the set of Takagi-Sugeno type fuzzy rules. The approach combines the best of fuzzy and conventional control theory. It enables linguistic interpretability (also called transparency) of both the plant model and the controller. In the case of linear systems and some class of nonlinear systems, engineers can in many cases directly apply well-known classical tools from the control theory both for analysis, and the design of closed-loop fuzzy control systems. Therefore the main objective of the book is to establish comprehensive and unified analytical foundations for fuzzy modeling using the Takagi-Sugeno rule scheme and their applications for fuzzy control, identification of some class of nonlinear dynamical processes and classification problem solver design.
