Multi-switching adaptive synchronization of two fractional-order chaotic systems with different structure and different order

In this work, we combine the active and adaptive control theories, and propose a novel synchronization scheme for a class of fractional-order chaotic systems with different structure and different order. Based on the new version of fractional-order Lyapunov stability theory, we design the adaptive controllers and updating laws of different switching. We use the fractional-order Lorenz chaotic system and the fractional-order Chen chaotic system as examples to analyze the multi-switching synchronization process for fractional-order chaotic systems with different structures and different orders. Finally, numerical simulations are also given to illustrate the effectiveness and validation of the proposed method, and the model uncertainties and external disturbances are added to the considered systems to verify the robustness of the proposed controllers.