Synchronization of uncertain fractional-order hyper-chaotic systems via a novel adaptive interval type-2 fuzzy active sliding mode controller

In this paper, a novel adaptive interval type-2 fuzzy active sliding mode control (AIT2FASMC) approach is proposed for synchronization of fractional-order hyper-chaotic systems. The synchronization is achieved in front of uncertainties facing the fuzzy logic controller (FLC) in fractional–order hyper-chaotic systems such as uncertainties in control outputs, uncertainties in inputs to the fuzzy logic controller, and linguistic uncertainties. Two fractional-order hyper-chaotic systems can be synchronized based on Lyapunov stability theorem by using direct AIT2FASMC approach. Also, the proposed method reduces the chattering phenomena in the control signal, significantly. This novel fractional-order sliding mode controller is proposed for robust stabilization/synchronization problem of a class of fractional-order hyper-chaotic systems in the presence of external noise. Type-2 fuzzy active sliding mode control $$\left( {FASMC}\right) $$FASMC have the ability to overcome the limitations of type-1 FASMC when system is corrupted by high levels of uncertainty. Finally, the proposed approach is applied to two identical and non-identical fractional-order hyper-chaotic systems when the slave system is perturbed by external noise. Simulation results show applicability and feasibility of the proposed finite-time control strategy.

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