On the equivalence of a table lookup (TL) technique and fuzzy neural network (FNN) with block pulse membership functions (BPMFs) and its application to water injection control of an automobile

Abstract

This paper presents an alternative method to design a fuzzy neural network (FNN) using a set of nonoverlapped block pulse membership functions (BMPFs), and this FNN with nonoverlapped BPMFs will be shown to be equivalent to the conventional table lookup (TL) technique. Therefore, the hidden links between TL and FNN techniques are revealed in this paper that provides a methodology to design a TL controller based on the FNN design concept. In order to do so, a new direct formula is first developed to generate the fuzzy rules from the premise part in FNN. This direct formula not only guarantees a one-to-one mapping that maps the fuzzy membership functions onto the fuzzy rules, but also alleviates the coding effort during hardware implementation. It is further elaborated that the FNN with nonoverlapped BPMFs has the advantage of faster online training that requires less computation time, but at the cost of more memory requirement to store the fuzzy rules. The application of this new approach has been applied successfully in the water injection control of a turbo-charged automobile with excellent results.