Theory of the Fuzzy Controller: A Brief Survey

This chapter focuses on a tutorial on the modern fuzzy controller. It discusses the internal workings of a basic fuzzy controller, and deals with Sugeno&s;s fuzzy controller separately from the other elementary fuzzy controllers. The chapter surveys the "extras", which include self-organizing, adaptive, predictive, self-regulating, fuzzy model based, and neural fuzzy controllers. It also surveys the known theoretical results on the fuzzy controller. These include the functional relationship between the defuzzified output and all the inputs to the fuzzy controller, limit theorems, and stability. A few researchers have noticed that if they increased the number of fuzzy numbers used for each input, hence increased the number of fuzzy control rules; there was little or no change in control of the process. Basic fuzzy controllers may be divided into two groups depending on how the fuzzy control rules are evaluated: as production rules in an expert system or as implications in approximate reasoning.