Control and synchronization for two Chua systems based on intuitionistic fuzzy control scheme: A comparative study

Abstract

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.

Control in the loop for synchronization of nonlinear chaotic systems via adaptive intuitionistic neuro-fuzzy: a comparative study

“…The stability analysis of the IFC system has been discussed in [35]. The main difference between IFC and AINF is that AINF has some parameters to be updated with the learning rates depending on the backpropagation method, which makes the stability of the AINF has been dependent on the learning rates.…”

“…This system was introduced by [49]. The dimensionless model of the piecewise linear Chua's oscillator has been heavily studied in many research as [35] and this model is defined as follows:…”

“…The vectors of error and the change of error are defined as The results of synchronization between the two chaotic systems based on AINF-PID would be represented in this section and compared with IFC-PID proposed in [35]. As mentioned in [35], the inputs have been chosen as e, ė in which e…”

“…The value of u 1 depends on the calculations based on the inputs e 1 , ė1 and the value of u 3 depends on the calculations based on the inputs e 3 , ė3 . Because this paper would be compared with [35], the same basic structure of the controller would be used in this paper with the same controller gains and the same initials of the membership and non-membership functions. Therefore, the fuzzy sets for the inputs have been selected to be in the Gaussian formula as shown in (3).…”

“…After that, many studies have been published in this field. Intuitionistic fuzzy has been recently studied in various fields as decision-making [32] and image enhancement [33]; also, intuitionistic fuzzy has a recent role in control nonlinear systems [34] and for synchronization of chaotic systems [35].…”