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Stability analysis in identification of interval type‐2 adaptive neuro‐fuzzy inference system: Contribution to a novel Lyapunov function
Author(s) -
Zabihi Shesh Poli Mohammad Mahdi,
Aliyari Shoorehdeli Mahdi,
Moarefianpour Ali
Publication year - 2019
Publication title -
expert systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 38
eISSN - 1468-0394
pISSN - 0266-4720
DOI - 10.1111/exsy.12457
Subject(s) - computer science , stability (learning theory) , lyapunov function , identifier , identification (biology) , fuzzy control system , adaptive neuro fuzzy inference system , antecedent (behavioral psychology) , control theory (sociology) , interval (graph theory) , fuzzy logic , artificial intelligence , machine learning , mathematics , control (management) , nonlinear system , psychology , developmental psychology , physics , botany , quantum mechanics , biology , programming language , combinatorics
Abstract In recent years, control research has strongly highlighted the issue of training stability in the identification of non‐linear systems. This paper investigates the stability analysis of an interval type‐2 adaptive neuro‐fuzzy inference system (IT2ANFIS) as an identifier through a novel Lyapunov function. In so doing, stability analysis is initially conducted on the IT2ANFIS identifier, while performing the online training of both the antecedent and the consequent parameters by the gradient descent (GD) algorithm. In addition, the same stability analysis is carried out when the antecedent and the consequent parameters are trained by GD and forgetting factor recursive least square (FRLS) algorithms, respectively (GD + FRLS). A novel Lyapunov function is proposed in this study in order for the identifier stability to attain the required conditions. These conditions determine the permissible boundaries for the covariance matrix and the learning rates at every iteration of the identification procedure. Stability analysis reveals that wide range of learning rates is obtained. Furthermore, simulation results indicate that when the permissible boundaries are selected according to the proposed stability analysis, a stable identification process with appropriate performance is achieved.