Adaptive hybrid projective synchronization between different fractional-order chaotic systems with parameter uncertainty and unknown bounded external disturbances

This paper investigates the hybrid projective synchronization problem between different fractional-order chaotic systems in the presence of system parameter uncertainty and unknown bounded external disturbances. By means of both the stability theory of fractional order differential system and adaptive control method, a novel robust controller and updating laws have been designed for achieving hybrid projective synchronization of the fractional-order chaotic systems without the knowledge of upper bounds of disturbances. The results of numerical simulation show the feasibility and effectiveness of the proposed scheme.