Synchronization of fractional-order hyper-chaotic systems based on a new adaptive sliding mode control

In this paper, a novel adaptive sliding mode approach for synchronization of fractional-order identical and non-identical chaotic and hyper-chaotic systems is proposed. The effects of unknown parameters and model uncertainties are also fully taken into account. The upper bound of the uncertainties is used to obtain the controller parameters. Here in this paper a novel sliding surface is proposed and its finite-time convergence to origin is analytically proved. Appropriate adaptation laws are obtained to undertake the unknown parameters of the controller. The stability of the resulting synchronization error system in a given finite-time is proved. Finally, particle swarm optimization algorithm is used for optimizing the controller parameters. Illustrative examples for a recently revealed 4-D fractional-order chaotic system are presented. This new 4-D fractional-order chaotic system has non chaotic behavior for its integer-order system and is different from the other previous fractional-order chaotic systems. Simulation results show the applicability and feasibility of the proposed finite-time control strategy. © 2015, Springer-Verlag Berlin Heidelberg.