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

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.

I. Introduction

The fuzzy neural network (FNN) has been shown to have tremendous impact on engineering applications in the last decade [1]–[4]. Several kinds of FNNs have also been developed for different kinds of applications, such as real-time intelligent adaptive control [5], [6], image processing [7], [8], etc. One of the advantages of FNNs is that it can be trained to suit the real physical environment with either offline or online trainings [9], [10]. Furthermore, the table lookup (TL) technique has been applied extensively for hardware implementation of engineering applications during the last decade [11]–[16]. However, the TL technique is a direct mapping approach without any embedded training strategy. Depending on the requirements of different applications, the FNN and TL techniques can both be applied successfully in engineering applications. To be more specific, fuzzy lookup tables were proposed in [11] to speed up the online learning fuzzy controller with a PD controller. However, the relationships between TL and FNN have never been discussed in a formal and systematic way. Therefore, the major purpose of this paper is to reveal the hidden links between TL and FNN techniques in a rigorous manner. For this to happen, a new direct formula will be first proposed to generate the fuzzy rules in FNN. Then, a special kind of FNN with block pulse membership functions (BPMFs) will be defined. Finally, the new direct formula will be adopted to show the equivalence of the FNN with BPMFs and TL techniques.