Open AccessAdaptive type‐2 fuzzy system for synchronisation and stabilisation of chaotic non‐linear fractional order systems
Author(s) -
Jafari Pouria,
Teshnehlab Mohammad,
TavakoliKakhki Mahsan
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0785
Subject(s) - control theory (sociology) , mathematics , controller (irrigation) , interval (graph theory) , fuzzy control system , adaptive neuro fuzzy inference system , fuzzy logic , stability (learning theory) , adaptive control , projection (relational algebra) , fuzzy set , computer science , algorithm , control (management) , artificial intelligence , biology , combinatorics , machine learning , agronomy
This study proposes an adaptive interval type‐2 Takagi–Sugeno–Kang (IT2 TSK) fuzzy system with a supervisory mode to control and stabilise a certain class of non‐linear fractional order systems. In this study, a fractional order adaptation law is derived which adjusts the free parameters and bounds them by utilising a projection algorithm. The global Mittag–Leffler stability of the closed‐loop system is proved in the sense that all the involved signals are uniformly bounded. Moreover, if the non‐linear system tends to be unstable, a supervisory controller starts cooperating with the adaptive IT2 TSK fuzzy controller to guarantee the stability of the closed‐loop system. In addition, a new inference mechanism for the adaptive IT2 TSK fuzzy system is introduced for which the antecedent part is chosen as a type‐2 fuzzy set and the consequent parameters are represented as interval sets. According to the practical nature of the proposed inference equation, it would be applicable in online and real‐time applications. Numerical simulations show the validity and effectiveness of the introduced control strategy for stabilisation and control of a general class of non‐linear fractional order systems perturbed by disturbance and uncertainty.