A Novel High-Order Fuzzy Systems with ‎Decomposition in to Zero-and First-Order Fuzzy ‎Structures in Nonlinear Dynamic Systems

Fuzzy modeling is a relatively new system modeling method with a proven efficiency record in various fields. Although zero- and first-order fuzzy systems are common due to their simplicity, their linear structure faces challenges when modeling nonlinear systems with state-variable interaction. These challenges include an increase in the number of rules and the inability to stabilize highly nonlinear systems. One solution is to use high-order fuzzy systems, which have a nonlinear structure and can represent model input interactions. In previous research, high-order fuzzy modeling has been investigated for static and nonlinear systems based on data, but such modeling has not been applied to dynamic systems with nonlinear nature which is a model of industrial processes. The present paper proposes a novel fuzzy structure inspired by the Taylor series expansion for dynamic systems with nonlinear state-space equations. This structure has a high degree of freedom in modeling complex nonlinear processes and can be adapted to the state-space equations of the system. The main novelty of this method is the conversion of a nonlinear high-order fuzzy structure into a set of first-order fuzzy structures. Another advantage is the ability to calculate the coefficients of the high-order fuzzy system from the Taylor series coefficients of the dynamic system’s model. Fuzzy systems have made various applications possible in the field of approximation. The present paper also proves the approximation ability and convergence of the proposed structure and determines its convergence criteria.