Synchronization of two different chaotic systems using chattering-free adaptive interval type-2 fuzzy sliding mode control

In this paper, we use an interval type-2 fuzzy logic system integrated with sliding mode control for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the sliding mode control (SMC) an interval type-2 fuzzy logic controller is used. In addition, an adaptive interval type-2 fuzzy approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic systems. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy systems. The stability analysis for the proposed control scheme is provided and simulation results compare the performance of proposed interval type-2 fuzzy controller with type-1 fuzzy controllers to verify the effectiveness of the proposed method.