Nonlinear Dynamical Systems Modelling and Identification Using Type-2 Fuzzy Logic - Metaheuristic Algorithms Based Approach

Abstract

This paper presents a novel type-2 fuzzy model for nonlinear dynamical systems. This method can deal with the curve fitting and computational time problems of type-2 fuzzy systems. It is based on interval type-2 fuzzy systems and it is comprised of a parallel interconnection of two type-2 sub fuzzy models. The first sub fuzzy model is the primary model, which represents an ordinary model with low resolution for the nonlinear dynamical system under consideration. To overcome resolution quality problem, and obtain a model with higher resolution, we will introduce a second type-2 fuzzy sub model called error model which will represent a model for the error modelling between the primary model and the real nonlinear dynamical system. As the error model represents uncertainty in the primary model, it’s suitable to minimize this uncertainty by simple subtraction of the error model output from the primary model output, which will lead to a parallel interconnection between them, giving then a unique whole final model possessing higher resolution. To apply this approach successfully, the model’s representation and identification are considered in this investigation using type-2 fuzzy auto regressive (T2FAR) and type-2 fuzzy auto regressive moving average (T2FARMA) models. Identification is achieved by innovative metaheuristic optimization algorithms, like as firefly and biogeography-based optimization algorithms. To evaluate the effectiveness of the proposed method, it will be tested on three types of nonlinear dynamical systems. Computer investigations indicate that the proposed model may significantly improves convergence and resolution.