Mittag–Leffler synchronization of fractional-order uncertain chaotic systems**Project supported by the National Natural Science Foundation of China (Grant No. 61171034) and the Zhejiang Provincial Natural Science Foundation of China (Grant No. R1110443).

Abstract

This paper deals with the synchronization of fractional-order chaotic systems with unknown parameters and unknown disturbances. An adaptive control scheme combined with fractional-order update laws is proposed. The asymptotic stability of the error system is proved in the sense of generalized Mittag–Leffler stability. The two fractional-order chaotic systems can be synchronized in the presence of model uncertainties and additive disturbances. Finally these new developments are illustrated in examples and numerical simulations are provided to demonstrate the effectiveness of the proposed control scheme.