Hopf bifurcation and synchronization of a five-dimensional self-exciting homopolar disc dynamo using a new fuzzy disturbance-observer-based terminal sliding mode control


Wei Z., Yousefpour A., Jahanshahi H., KOCAMAZ U. E. , Moroz I.

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, vol.358, no.1, pp.814-833, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 358 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1016/j.jfranklin.2020.11.011
  • Journal Name: JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Periodicals Index Online, Aerospace Database, Communication Abstracts, INSPEC, Metadex, MLA - Modern Language Association Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.814-833
  • Bursa Uludag University Affiliated: Yes

Abstract

Having found hidden hyperchaos in a 5D self-exciting homopolar disc dynamo, we study the existence of a Hopf bifurcation, which leads to unstable limit cycles bifurcating from a stable equilibrium. Hidden chaos with only stable equilibria can be observed from the Hopf bifurcation: a typical way to enable hidden attractors to be located. We then provide a new fuzzy controller, and a fast fuzzy disturbance observer, based on terminal sliding mode control for synchronization of the hyperchaotic system. Fuzzy inference is considered to weaken the chattering phenomena. Using Lyapunov stability theory, the stability of the closed-loop system is proved. Finally, simulations of synchronization are illustrated to show the efficient performance of the designed control method via external disturbances and dynamic uncertainties. Crown Copyright (C) 2020 Published by Elsevier Ltd on behalf of The Franklin Institute. All rights reserved.