Design an adaptive sliding mode controller for drive-response synchronization of two different uncertain fractional-order chaotic systems with fully unknown parameters

In this paper, design an adaptive sliding mode controller (ASMC) for master–slave synchronization of two different fractional-order chaotic systems with fully unknown parameters, uncertainties and external disturbances is proposed. The bounds of the unknown parameters, uncertainties and external disturbances are assumed to be unknown in advance. Appropriate adaptive laws are designed to tackle the unknown parameters, uncertainties and external disturbances. Based on the adaptive laws, the ASMC is constructed in order to ensure the occurrence of the sliding motion and synchronization of two different fractional-order systems. The analytical conditions for synchronization of the systems are obtained by utilizing Laplace transform. Finally, numerical examples are provided to illustrate the effectiveness of the proposed ASMC scheme.