Analytical Methods in Fuzzy Modeling and Control

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.