Modified function projective synchronization of fractional-order hyperchaotic systems based on active sliding mode control

Abstract

Considering the time-varying scaling function matrix and system disturbances, a new sliding mode control strategy is proposed to realize modified function projective synchronization (MFPS) of two different fractional-order hyperchaotic systems, meanwhile improve the control robustness of synchronization system. From the MFPS error equations, combining a proper fractional-order exponential reaching raw, an active controller for MFPS is derived out via sliding mode control technology. By mean of the stability theorem, the asymptotic stability of synchronization error system is proved. Simulation results of the MFPS between fractional-order hyperchaoticLorenz system and Chen system demonstrate the validity of the presented method.