Petri type 2 fuzzy neural networks approximator for adaptive control of uncertain non‐linear systems

Abstract

In this study, the authors developed a novel universal approximator by the integration of Petri networks into type 2 fuzzy neural networks (T2FNN). T2FNN involve large number of rules, which result in heavy computational burden and great computation time. By incorporating Petri layers to optimise the number of rules; these two drawbacks could be very well overcome. Moreover, a new inference type 2 fuzzy system was developed to reduce the time consumed in the iterative K–M inference procedure, and to increase the approximation accuracy. The proposed inference engine is based on the use of an adaptive modulation of the upper and the lower outputs. The Petri type 2 fuzzy neural networks (PT2FNN) approximator was used to approximate the adaptive control for uncertain single-input single-output non-linear system. The stability of the closed-loop system was proven and demonstrated using the Lyaponov approach. Comparative studies of the proposed PT2FNN approximator with type 1 fuzzy neural network and T2FNN were performed. The performances of PT2FNN over the two types of the fuzzy system were shown on the inverted pendulum system.