Structure analysis and universal approximation of IT2 TS FLC using NT algorithm

Abstract

The analytical structure plays an important role in system design and stability analysis of FLC. Structure analysis of traditional IT2 TS FLCs using Zadeh min operator and KM algorithm requires multiple IC dividing, which results in complex calculation and cumbersome parameter adjustment. This article proposes a new IT2 TS FLC by adopting product-type operator and NT algorithm. The proposed controller has such advantages: 1)use product-type operator to skip the partitioning in fuzzy inference process;2) use NT algorithm to avoid determining switching points and sorting rule consequents in type-reduction process. Then, the controller is proved to be universal approximator and sufficient condition is deduced. Finally, we derive the analytical structure of the controller by substituting the parameters, and study the relationship between the uncertainty parameter θ and the analytical structure when the rule consequents are symmetric or asymmetric. Both the computational costs during operation and the computational workload for structural analysis can be reduced significantly by using the new FLC.