An Empirical Analysis of One Type of Direct Adaptive Fuzzy Control

This chapter will address, both in an analytical and experimental ways, various issues related to the automatic construction and on-line adaptation of fuzzy controllers. First we will show a DAFC ( Direct Adaptive Fuzzy Control), i.e., an adaptive control methodology requiring a minimal knowledge of the process to be coupled with, can be derived in a way very reminiscent of neurocontrol methods. Indeed a main point to be argued and illustrated in this chapter is the case to import methods and ideas emerging in the connectionist community for control applications as soon as the fuzzy controller is supplied with a gradient method for the automatic tunning of its parameters (such as the membership functions) akin to the well known backpropagation for multilayer neural nets. Since fuzzy PID is one of the most popular fields of investigation in the fuzzy control community with researchers trying to understand better the kind of non-linear extrapolation the fuzzyfication of classical PID can provide, we will show how to extend DAFC to fuzzy PID. An adaptive fuzzy satisfies both objectives to make the resulting control and to offer a method for automatic discovery as well as mechanisms of adaptation for processes in varying environments. Besides, it has been recently shown that radial-basis neural networks were nearly equivalent to Sugeno’s type of fuzzy systems (the only type we are using) making any fuzzy-neural comparison and merging often very redundant and confusing. We will finally attempt to clarify what is alike and what is different between a Sugeno’s fuzzy system and a radial-basis neural net.