This paper presents control and synchronization for two nonlinear chaotic systems in the presence of uncertainties and external disturbances based on an intuitionistic fuzzy control (IFC) scheme. Two classes of Chua and cubic Chua oscillators have been formulated as master and slave respectively. The master and slave systems have different initial conditions and parameters, which leads to the butterfly effect that rules the chaotic systems’ behaviour. IFC scheme is chosen as a different method that has not been used before to control and synchronize Chua and cubic Chua oscillators. The main objective of the IFC scheme is to collect more information about the system and provide flexibility for the controller that increases the robustness of the control system to uncertainties in the structure of the chaotic systems. The stability analysis of the overall system is guaranteed using Routh-Hurwitz and Lyapunov criteria. The simulation results accomplished to evaluate the effectiveness of the proposed control and to demonstrate its reliability to control Chua’s circuit system with a comparative study.

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This paper proposes control in the loop (CIL) for the synchronization between two nonlinear chaotic systems at the existence of uncertainties and disturbances using an adaptive intuitionistic neuro-fuzzy (AINF) control scheme. The chaotic systems have been subedited as one is the master and the other is the slave. They both have different initial conditions and parameters. The variation in the initial conditions leads to the butterfly effect, the concept that is well known in the chaos field and means that both systems diverge over time. Therefore, AINF control scheme has been proposed in this paper as a powerful scheme to get over this problem effectively. The main objective of using the AINF control scheme is that it collects the features of its contents. As the intuitionistic fuzzy gives the system flexibility and helps the controller collecting more information about the problem. The neural networks give the controller the ability to learn over time. The experimental results were obtained to verify the applicability and effectiveness of the proposed control scheme against external disturbance and model uncertainties with comparative study.

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.

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