Robust ${H_\\infty }$-Based Synchronization of the Fractional-Order Chaotic Systems by Using New Self-Evolving Nonsingleton Type-2 Fuzzy Neural Networks

In this paper, a novel ${H_\\infty }$ -based adaptive fuzzy control is presented for the synchronization of fractional-order chaotic systems. A self-evolving nonsingleton type-2 fuzzy neural network (SE-NST2FNN) is proposed for the estimation of the unknown functions in the dynamics of the system. The effects of the approximation error and the external disturbances are eliminated by designing an adaptive compensator, such that the ${H_\\infty }$ norm of the synchronization error is minimized and asymptotically stability is achieved. The consequent parameters of SE-NST2FNN are tuned based on the adaptation laws that are derived from Lyapunov stability analysis. The antecedent part and the rule database of SE-NST2FNN are optimized based on a clustering method and the modified invasive weed optimization algorithm, respectively. The effectiveness of proposed control scheme is verified by simulation examples.