Publication: Hopf bifurcation and synchronization of a five-dimensional self-exciting homopolar disc dynamo using a new fuzzy disturbance-observer-based terminal sliding mode control
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Date
2021-01
Authors
Kocamaz, Uğur Erkin
Authors
Wei, Zhouchao
Yousefpour, Amin
Jahanshahi, Hadi
Moroz, Irene
Journal Title
Journal ISSN
Volume Title
Publisher
Pergamon-Elsevier Science LTD
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.
Description
Keywords
4-Dimensional chaotic system, Unknown-parameters, Adaptive-control, Design, Feedback, Closed loop systems, Fuzzy inference, Interactive devices, Sliding mode control, Synchronization, Dynamic uncertainty, External disturbances, Fuzzy disturbance observers, Hyper-chaotic systems, Lyapunov stability theory, Stable equilibrium, Terminal sliding mode control, Unstable limit cycles, Hopf bifurcation
Citation
Kocamaz, U.E. (2021). "Hopf bifurcation and synchronization of a five-dimensional self-exciting homopolar disc dynamo using a new fuzzy disturbance-observer-based terminal sliding mode control".Journal of the Franklin Institute, 358(1), 814-833.