A modified sliding mode approach for synchronization of fractional-order chaotic/hyperchaotic systems by using new self-structuring hierarchical type-2 fuzzy neural network

This paper presents a new adaptive sliding mode control approach for the synchronization of the uncertain fractional-order chaotic systems. A self-structuring hierarchical type-2 fuzzy neural network (SHT2FNN) is proposed for estimation of uncertainties. Also the switching control action in the conventional sliding mode scheme is replaced by combination type-2 fuzzy neural network (T2FNN) with hyperbolic tangent function. In SHT2FNN, the number of rules is determined by a proposed algorithm. Adaptation laws of all trainable parameters of T2FNN and the consequent parameters of SHT2FNN, are derived based on Lyapunov stability analysis. The simulation results on two kind systems: Genio-Tesi and Coullet System and fractional-order hyper-chaotic Lorenz system, confirm the efficacy of the proposed scheme in synchronization of the uncertain fractional-order hyperchaotic and fractional-order chaotic systems.The proposed controller is robust against the approximation error and external disturbance. The proposed self-structuring algorithm in this paper is simple and it can be applied in the high dimensional problems. Furthermore, the proposed algorithm can delete unimportant rules. Adjusting the structure of the T2FNN in the hierarchical form ensures that the estimation error is very small so it can be negligible. Furthermore, the proposed strategy guarantees the robustness of controller.