Design of adaptive intuitionistic fuzzy controller for synchronisation of uncertain chaotic systems

Abstract

This study presents the synchronisation between two non-linear Lorenz chaotic systems using an adaptive intuitionistic fuzzy controller (AIFC). This problem is solved in the presence of external disturbances and uncertainties. Two classes of Lorenz systems have been formulated one as the master and the other as the slave. The master and slave systems have different initial conditions. Under different initial conditions, both systems diverge. This is called the butterfly effect that rules the behaviour of chaotic systems. AIFC is chosen as a different method that has not been used before to synchronise the chaotic systems. The scaling factors of the inputs and the output of the intuitionistic fuzzy controller (IFC) are tuned using the artificial bee colony (ABC) algorithm depending on a specified objective function. Then IFC stability is studied when it is applied to synchronise the Lorenz system. The simulation results achieved to assess the adequacy of the proposed control and to exhibit its dependability to synchronise the Lorenz system.

Keywords

• fuzzy set theory
• fuzzy control
• synchronisation
• chaos
• nonlinear control systems
• uncertain systems
• adaptive intuitionistic fuzzy controller
• synchronisation
• uncertain chaotic systems
• lorenz chaotic systems
• aifc
• external disturbances
• uncertainties
• slave systems
• systems diverge
• ifc stability