Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface

Abstract

This paper addresses the problem of generalized finite-time function projective synchronization (GFFPS) of fractionalorder chaotic systems. A modified fractional nonsingular terminal sliding mode surface and an appropriate robust fractional sliding mode control law are proposed, taking into account the effects of model uncertainties and of the external disturbances. An appropriate Lyapunov functional candidate is used to prove the finite-time existence of the sliding motion. Compared with the existing nonsingular sliding mode surface, our sliding mode surface permits to reduce the settling time of synchronization. Finally, some numerical simulations taking into consideration the Gaussian white noise produced by the electrical line are presented to demonstrate the effectiveness and applicability of the proposed technique.

Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization

“…This time synchronization is important for an engineer because it permits a better determination of parameters which can entail the synchronization of coupled systems [33]. In this context, there is a keen work in the study of finite-time chaos synchronization [34,35] and gradually of fractionalorder systems [33,36,37]. To the best of our knowledge, except some works like those defined in [21], [22] and more recently in [25] to mention only those who studied stability in the non-adaptive case, no further work has been done in respect to adaptive synchronization case.…”