Backstepping control for combined function projective synchronization among fractional order chaotic systems with uncertainties and external disturbances

Abstract

In the present chapter the combined function projective synchronization among fractional order chaotic systems in the presence of uncertain parameters and external disturbances using backstepping control method is investigated. The chaotic attractors of the systems are found for fractional-order time derivative, which is described in Caputo sense. A new lemma of Caputo derivatives is used to design the controller based on Lyapunov stability theory. During the combined function projective synchronization among the non-identical fractional order systems, the Lorenz, Rossler and Chen systems are taken to illustrate the effectiveness of the considered method. Numerical simulation and graphical results for different particular cases clearly exhibit that the method with this new procedure is easy to implement and reliable for synchronization of non-identical fractional order chaotic systems. © 2018, Springer International Publishing AG.