Synchronization of uncertain fractional order chaotic systems via adaptive interval type-2 fuzzy sliding mode control

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AITFSMC) is proposed to handle high level uncertainties facing the fuzzy logic controller (FLC) in dynamic fractional order chaotic systems such as uncertainties in inputs to the FLC, uncertainties in control outputs, linguistic uncertainties and uncertainties associated with the noisy training data. Based on the learning algorithm combining Lyapunov approach and sliding mode control, free parameters of the AITSMC can be tuned on line by output feedback control law and adaptive law to synchronize two different uncertain fractional order chaotic systems. Meanwhile, the chattering phenomena in the control efforts can be reduced. During the design procedure, not only the stability and robustness can be guaranteed but also the external disturbance on the synchronization error can be attenuated. The numerical simulation is performed to illustrate the effectiveness of the proposed control strategy.