Active disturbance rejection control for synchronization of different fractional-order chaotic systems

This paper investigates the fractional-order active disturbance rejection control for the synchronization of two different fractional-order chaotic systems. By the fractional-order extended state observers, the nonlinear dynamics in the synchronization error equations for each subsystems are estimated in real time. Compensating the nonlinear estimations into controllers, the active disturbance rejection controllers are designed to achieve the synchronization. Finally, two examples of synchronization issues on different fractional-order chaotic systems are provided to verify that the fractional-order ADRC is irrelevant with the nonlinear dynamics in the fractional-order chaotic systems. The proposed controllers can achieve the synchronization and estimate the nonlinear dynamics effectively for different fractional-order chaotic systems.