Adaptive Interval Type-2 Fuzzy PI Sliding Mode Control with optimization of membership functions using genetic algorithm

Abstract

A new stable Adaptive Interval Type-2 Fuzzy Proportional Integral Sliding Mode Controller (AI2FPISMC) is introduced here to control a class of nonlinear systems. The proposed method is based on interval type-2 fuzzy logic system (IT2FLS) whose antecedent and consequent membership functions are interval type-2 fuzzy sets. IT2FLS is utilized to approximate unknown nonlinear functions. To achieve high performance, optimizing membership functions (MFs) of interval type-2 fuzzy sets (IT2FS) is required. Genetic algorithm (GA) is a parallel search optimization method; that here contributes to optimize the MFs. In order to cope with the chattering of sliding mode controller, PI control law is proposed and Lyapunov analysis is utilized to prove asymptotic stability of the proposed approach. The adaptation laws are derived using Lyapunov approach. Two nonlinear system simulation examples are presented to verify the effectiveness of the proposed method, and their results confirm the optimization merits.