The Synchronization of Hyperchaotic Systems Using a Novel Interval Type-2 Fuzzy Neural Network Controller

Abstract

This paper proposed a novel interval type-2 fuzzy neural network controller (NT2FC) to synchronize 5-D hyperchaotic systems with noise disturbance and system uncertainties. In the proposed controller, the type 2 fuzzy set is designed with the 3-dimensional Gaussian membership functions (3DGMFs) to increase the system’s ability to respond to uncertainty. The parameters of the NT2FC controller are updated online via adaptation laws, which are built based on the gradient descent approach. The system stability is ensured through the Lyapunov stability analysis. In addition, the modified Jaya algorithm (MJA) is applied to optimize the learning rates in adaptation laws. Finally, the efficiency of the proposed NT2FC is examined by the numerical simulation of the hyperchaotic system’s synchronization.

Keywords

• 5-D hyperchaotic systems
• fuzzy neural network
• type-2 fuzzy system
• 3DGMFs
• Jaya algorithm