Learning control using fuzzified self-organizing radial basis function network

Abstract

This note describes an approach to integrating fuzzy reasoning systems with radial basis function (RBF) networks and shows how the integrated network can be employed as a multivariable self-organizing and self-learning fuzzy controller. In particular, by drawing some equivalence between a simplified fuzzy control algorithm (SFCA) and a RBF network, we conclude that the RBF network can be interpreted in the context of fuzzy systems and can be naturally fuzzified into a class of more general networks, referred to as FBFN, with a variety of basis functions (not necessarily globally radial) synthesized from each dimension by fuzzy logical operators. On the other hand, as a result of natural generalization from RBF to SFCA, we claim that the fuzzy system like RBF is capable of universal approximation. Next, the FBFN is used as a multivariable rule-based controller but with an assumption that no rule-base exists, leading to a challenging problem of how to construct such as rule-base directly from the control environment. We propose a simple and systematic approach to performing this task by using a fuzzified competitive self-organizing scheme and incorporating an iterative learning control algorithm into the system. We have applied the approach to a problem of multivariable blood pressure control with a FBFN-based controller having six inputs and two outputs, representing a complicated control structure.