The synchronization of fractional order chaotic systems with different orders based on adaptive sliding mode control

Abstract

In this paper, based on sliding mode control and adaptive control theory, the synchronization of two different fractional order chaotic systems is investigated. First, a fractional sliding surface with strong robustness is designed and a suitable adaptive sliding controller is constructed, then the error states of the systems are controlled to the sliding surface via the method to guarantee the synchronized behaviors between two fractional chaotic systems. Numerical simulations on the hyper Chen chaotic systems and Chen chaotic system are also carried out respectively. Simulation results show that the generalized errors tend to zero after a short time, and the effectiveness and feasibility of this method are well verified.